Faster access than browser!
222 relations: Abelian group, Adjoint functors, Algebraic closure, Algebraic geometry, Algebraic Geometry (book), Antihomomorphism, Arithmetic, Associative algebra, Autonomous category, Étale cohomology, Basis (linear algebra), Bilinear form, Bilinear map, Birkhoff's representation theorem, C*-algebra, Cambridge University Press, Cartesian product, Categories for the Working Mathematician, Category (mathematics), Category theory, Character group, Circle group, Closed set, Closure (topology), Cofibration, Coherent duality, Coherent sheaf, Cohomology, Commutative algebra, Commutative ring, Compact group, Compact space, Compact-open topology, Complement (set theory), Complete Heyting algebra, Complex manifold, Complex number, Computational geometry, Constant sheaf, Converse relation, Convex hull, Convex polytope, Convex set, Convolution, Coproduct, CW complex, De Morgan's laws, De Rham cohomology, Delaunay triangulation, Derived category, ..., Desargues's theorem, Differential form, Differential operator, Dimension (vector space), Direct product, Direct sum of groups, Discrete group, Disjoint union, Distribution (mathematics), Distributive lattice, Division ring, Dual (category theory), Dual abelian variety, Dual basis, Dual code, Dual cone and polar cone, Dual graph, Dual matroid, Dual norm, Dual number, Dual polyhedron, Dual space, Duality (electrical circuits), Duality (optimization), Duality (order theory), Duality (projective geometry), Dualizing module, Dualizing sheaf, Electric field, Epimorphism, Equivalence of categories, Exterior algebra, Fibration, Field (mathematics), Filter (mathematics), Finite field, Fixed point (mathematics), Fourier analysis, Fourier transform, Function composition, Function space, Functor, Fundamental theorem of Galois theory, G-module, Galois cohomology, Galois connection, Galois extension, Galois group, Galois theory, Gelfand representation, Geometric transformation, Geometry, Global field, Graph embedding, Group cohomology, Group homomorphism, Half-space (geometry), Hamiltonian mechanics, Hausdorff space, Heyting algebra, Hilbert space, Hodge star operator, Hom functor, Homological algebra, Homological mirror symmetry, Homology (mathematics), Hypoelliptic operator, Ideal (order theory), If and only if, Image functors for sheaves, Injective module, Inner product space, Integer, Interior (topology), Intersection homology, Intersection number, Involution (mathematics), Isomorphism, John Wiley & Sons, Koszul duality, Kripke semantics, Lagrangian mechanics, Langlands dual group, Laplace transform, Lattice (group), Lebesgue integration, Legendre transformation, Limit (category theory), Linear algebra, Linear map, Linear programming, Line–line intersection, List of dualities, Local field, Local Tate duality, Locally compact space, Lp space, Magnetic field, Manifold, Mathematical analysis, Mathematical optimization, Mathematics, Matlis duality, Matroid, Maximal and minimal elements, Maxwell's equations, Michael Atiyah, Modal logic, Model category, Module (mathematics), Momentum, Monomorphism, Negation, Noncommutative geometry, Open set, Opposite category, Order isomorphism, Orthogonality, Pairing, Partial differential equation, Partially ordered set, Planar graph, Platonic solid, Poincaré duality, Pole and polar, Pontryagin duality, Positive definiteness, Power set, Princeton University Press, Profinite group, Projective module, Projective plane, Projective variety, Pullback (category theory), Quantifier (logic), Quantum mechanics, Quotient module, Real number, Reflexive space, Riemannian geometry, Riemannian manifold, Riesz representation theorem, Ring homomorphism, Ringed space, S-duality, Scheme (mathematics), Serre duality, Sheaf cohomology, Singular homology, Singular point of an algebraic variety, Sober space, Spectrum, Spectrum of a ring, Springer Science+Business Media, Stone duality, Subset, T-duality, Tangent space, Tannaka–Krein duality, Temporal logic, The Princeton Companion to Mathematics, Topological group, Topological vector space, Topology, Toric variety, Upper and lower bounds, Upper set, Vector space, Velocity, Verdier duality, Vertex (geometry), Voronoi diagram. Expand index (172 more) »
Abelian group
In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.
New!!: Duality (mathematics) and Abelian group · See more »
Adjoint functors
In mathematics, specifically category theory, adjunction is a possible relationship between two functors.
New!!: Duality (mathematics) and Adjoint functors · See more »
Algebraic closure
In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed.
New!!: Duality (mathematics) and Algebraic closure · See more »
Algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
New!!: Duality (mathematics) and Algebraic geometry · See more »
Algebraic Geometry (book)
Algebraic Geometry is an influential, algebraic geometry textbook written by Robin Hartshorne and published by Springer-Verlag in 1977.
New!!: Duality (mathematics) and Algebraic Geometry (book) · See more »
Antihomomorphism
In mathematics, an antihomomorphism is a type of function defined on sets with multiplication that reverses the order of multiplication.
New!!: Duality (mathematics) and Antihomomorphism · See more »
Arithmetic
Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.
New!!: Duality (mathematics) and Arithmetic · See more »
Associative algebra
In mathematics, an associative algebra is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field.
New!!: Duality (mathematics) and Associative algebra · See more »
Autonomous category
In mathematics, an autonomous category is a monoidal category where dual objects exist.
New!!: Duality (mathematics) and Autonomous category · See more »
Étale cohomology
In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil conjectures.
New!!: Duality (mathematics) and Étale cohomology · See more »
Basis (linear algebra)
In mathematics, a set of elements (vectors) in a vector space V is called a basis, or a set of, if the vectors are linearly independent and every vector in the vector space is a linear combination of this set.
New!!: Duality (mathematics) and Basis (linear algebra) · See more »
Bilinear form
In mathematics, more specifically in abstract algebra and linear algebra, a bilinear form on a vector space V is a bilinear map, where K is the field of scalars.
New!!: Duality (mathematics) and Bilinear form · See more »
Bilinear map
In mathematics, a bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each of its arguments.
New!!: Duality (mathematics) and Bilinear map · See more »
Birkhoff's representation theorem
In mathematics, Birkhoff's representation theorem for distributive lattices states that the elements of any finite distributive lattice can be represented as finite sets, in such a way that the lattice operations correspond to unions and intersections of sets.
New!!: Duality (mathematics) and Birkhoff's representation theorem · See more »
C*-algebra
C∗-algebras (pronounced "C-star") are an area of research in functional analysis, a branch of mathematics.
New!!: Duality (mathematics) and C*-algebra · See more »
Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
New!!: Duality (mathematics) and Cambridge University Press · See more »
Cartesian product
In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.
New!!: Duality (mathematics) and Cartesian product · See more »
Categories for the Working Mathematician
Categories for the Working Mathematician (CWM) is a textbook in category theory written by American mathematician Saunders Mac Lane, who cofounded the subject together with Samuel Eilenberg.
New!!: Duality (mathematics) and Categories for the Working Mathematician · See more »
Category (mathematics)
In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is an algebraic structure similar to a group but without requiring inverse or closure properties.
New!!: Duality (mathematics) and Category (mathematics) · See more »
Category theory
Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).
New!!: Duality (mathematics) and Category theory · See more »
Character group
In mathematics, a character group is the group of representations of a group by complex-valued functions.
New!!: Duality (mathematics) and Character group · See more »
Circle group
In mathematics, the circle group, denoted by T, is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers The circle group forms a subgroup of C×, the multiplicative group of all nonzero complex numbers.
New!!: Duality (mathematics) and Circle group · See more »
Closed set
In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set.
New!!: Duality (mathematics) and Closed set · See more »
Closure (topology)
In mathematics, the closure of a subset S of points in a topological space consists of all points in S together with all limit points of S. The closure of S may equivalently be defined as the union of S and its boundary, and also as the intersection of all closed sets containing S. Intuitively, the closure can be thought of as all the points that are either in S or "near" S. A point which is in the closure of S is a point of closure of S. The notion of closure is in many ways dual to the notion of interior.
New!!: Duality (mathematics) and Closure (topology) · See more »
Cofibration
In mathematics, in particular homotopy theory, a continuous mapping where A and X are topological spaces, is a cofibration if it satisfies the homotopy extension property with respect to all spaces Y. This definition is dual to that of a fibration, which is required to satisfy the homotopy lifting property with respect to all spaces.
New!!: Duality (mathematics) and Cofibration · See more »
Coherent duality
In mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex manifold theory, as well as some aspects of commutative algebra that are part of the 'local' theory.
New!!: Duality (mathematics) and Coherent duality · See more »
Coherent sheaf
In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space.
New!!: Duality (mathematics) and Coherent sheaf · See more »
Cohomology
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to a topological space, often defined from a cochain complex.
New!!: Duality (mathematics) and Cohomology · See more »
Commutative algebra
Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.
New!!: Duality (mathematics) and Commutative algebra · See more »
Commutative ring
In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.
New!!: Duality (mathematics) and Commutative ring · See more »
Compact group
In mathematics, a compact (topological) group is a topological group whose topology is compact.
New!!: Duality (mathematics) and Compact group · See more »
Compact space
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
New!!: Duality (mathematics) and Compact space · See more »
Compact-open topology
In mathematics, the compact-open topology is a topology defined on the set of continuous maps between two topological spaces.
New!!: Duality (mathematics) and Compact-open topology · See more »
Complement (set theory)
In set theory, the complement of a set refers to elements not in.
New!!: Duality (mathematics) and Complement (set theory) · See more »
Complete Heyting algebra
In mathematics, especially in order theory, a complete Heyting algebra is a Heyting algebra that is complete as a lattice.
New!!: Duality (mathematics) and Complete Heyting algebra · See more »
Complex manifold
In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic.
New!!: Duality (mathematics) and Complex manifold · See more »
Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
New!!: Duality (mathematics) and Complex number · See more »
Computational geometry
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry.
New!!: Duality (mathematics) and Computational geometry · See more »
Constant sheaf
In mathematics, the constant sheaf on a topological space X associated to a set A is a sheaf of sets on X whose stalks are all equal to A. It is denoted by or AX.
New!!: Duality (mathematics) and Constant sheaf · See more »
Converse relation
In mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation.
New!!: Duality (mathematics) and Converse relation · See more »
Convex hull
In mathematics, the convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X., p. 3.
New!!: Duality (mathematics) and Convex hull · See more »
Convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.
New!!: Duality (mathematics) and Convex polytope · See more »
Convex set
In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.
New!!: Duality (mathematics) and Convex set · See more »
Convolution
In mathematics (and, in particular, functional analysis) convolution is a mathematical operation on two functions (f and g) to produce a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.
New!!: Duality (mathematics) and Convolution · See more »
Coproduct
In category theory, the coproduct, or categorical sum, is a category-theoretic construction which includes as examples the disjoint union of sets and of topological spaces, the free product of groups, and the direct sum of modules and vector spaces.
New!!: Duality (mathematics) and Coproduct · See more »
CW complex
In topology, a CW complex is a type of topological space introduced by J. H. C. Whitehead to meet the needs of homotopy theory.
New!!: Duality (mathematics) and CW complex · See more »
De Morgan's laws
In propositional logic and boolean algebra, De Morgan's laws are a pair of transformation rules that are both valid rules of inference.
New!!: Duality (mathematics) and De Morgan's laws · See more »
De Rham cohomology
In mathematics, de Rham cohomology (after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of expressing basic topological information about smooth manifolds in a form particularly adapted to computation and the concrete representation of cohomology classes.
New!!: Duality (mathematics) and De Rham cohomology · See more »
Delaunay triangulation
In mathematics and computational geometry, a Delaunay triangulation (also known as a Delone triangulation) for a given set P of discrete points in a plane is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P).
New!!: Duality (mathematics) and Delaunay triangulation · See more »
Derived category
In mathematics, the derived category D(A) of an abelian category A is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on A. The construction proceeds on the basis that the objects of D(A) should be chain complexes in A, with two such chain complexes considered isomorphic when there is a chain map that induces an isomorphism on the level of homology of the chain complexes.
New!!: Duality (mathematics) and Derived category · See more »
Desargues's theorem
In projective geometry, Desargues's theorem, named after Girard Desargues, states: Denote the three vertices of one triangle by and, and those of the other by and.
New!!: Duality (mathematics) and Desargues's theorem · See more »
Differential form
In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates.
New!!: Duality (mathematics) and Differential form · See more »
Differential operator
In mathematics, a differential operator is an operator defined as a function of the differentiation operator.
New!!: Duality (mathematics) and Differential operator · See more »
Dimension (vector space)
In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.
New!!: Duality (mathematics) and Dimension (vector space) · See more »
Direct product
In mathematics, one can often define a direct product of objects already known, giving a new one.
New!!: Duality (mathematics) and Direct product · See more »
Direct sum of groups
In mathematics, a group G is called the direct sum of two subgroups H1 and H2 if.
New!!: Duality (mathematics) and Direct sum of groups · See more »
Discrete group
In mathematics, a discrete subgroup of a topological group G is a subgroup H such that there is an open cover of G in which every open subset contains exactly one element of H; in other words, the subspace topology of H in G is the discrete topology.
New!!: Duality (mathematics) and Discrete group · See more »
Disjoint union
In set theory, the disjoint union (or discriminated union) of a family of sets is a modified union operation that indexes the elements according to which set they originated in.
New!!: Duality (mathematics) and Disjoint union · See more »
Distribution (mathematics)
Distributions (or generalized functions) are objects that generalize the classical notion of functions in mathematical analysis.
New!!: Duality (mathematics) and Distribution (mathematics) · See more »
Distributive lattice
In mathematics, a distributive lattice is a lattice in which the operations of join and meet distribute over each other.
New!!: Duality (mathematics) and Distributive lattice · See more »
Division ring
In abstract algebra, a division ring, also called a skew field, is a ring in which division is possible.
New!!: Duality (mathematics) and Division ring · See more »
Dual (category theory)
In category theory, a branch of mathematics, duality is a correspondence between the properties of a category C and the dual properties of the opposite category Cop.
New!!: Duality (mathematics) and Dual (category theory) · See more »
Dual abelian variety
In mathematics, a dual abelian variety can be defined from an abelian variety A, defined over a field K.
New!!: Duality (mathematics) and Dual abelian variety · See more »
Dual basis
In linear algebra, given a vector space V with a basis B of vectors indexed by an index set I (the cardinality of I is the dimensionality of V), its dual set is a set B∗ of vectors in the dual space V∗ with the same index set I such that B and B∗ form a biorthogonal system.
New!!: Duality (mathematics) and Dual basis · See more »
Dual code
In coding theory, the dual code of a linear code is the linear code defined by where is a scalar product.
New!!: Duality (mathematics) and Dual code · See more »
Dual cone and polar cone
Dual cone and polar cone are closely related concepts in convex analysis, a branch of mathematics.
New!!: Duality (mathematics) and Dual cone and polar cone · See more »
Dual graph
In the mathematical discipline of graph theory, the dual graph of a plane graph is a graph that has a vertex for each face of.
New!!: Duality (mathematics) and Dual graph · See more »
Dual matroid
In matroid theory, the dual of a matroid M is another matroid M^\ast that has the same elements as M, and in which a set is independent if and only if M has a basis set disjoint from it.
New!!: Duality (mathematics) and Dual matroid · See more »
Dual norm
In functional analysis, the dual norm is a measure of the "size" of continuous linear functionals defined on a normed space.
New!!: Duality (mathematics) and Dual norm · See more »
Dual number
In linear algebra, the dual numbers extend the real numbers by adjoining one new element ε with the property ε2.
New!!: Duality (mathematics) and Dual number · See more »
Dual polyhedron
In geometry, any polyhedron is associated with a second dual figure, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.
New!!: Duality (mathematics) and Dual polyhedron · See more »
Dual space
In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V, together with the vector space structure of pointwise addition and scalar multiplication by constants.
New!!: Duality (mathematics) and Dual space · See more »
Duality (electrical circuits)
In electrical engineering, electrical terms are associated into pairs called duals.
New!!: Duality (mathematics) and Duality (electrical circuits) · See more »
Duality (optimization)
In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem.
New!!: Duality (mathematics) and Duality (optimization) · See more »
Duality (order theory)
In the mathematical area of order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted by Pop or Pd.
New!!: Duality (mathematics) and Duality (order theory) · See more »
Duality (projective geometry)
In geometry, a striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this concept.
New!!: Duality (mathematics) and Duality (projective geometry) · See more »
Dualizing module
In abstract algebra, a dualizing module, also called a canonical module, is a module over a commutative ring that is analogous to the canonical bundle of a smooth variety.
New!!: Duality (mathematics) and Dualizing module · See more »
Dualizing sheaf
In algebraic geometry, the dualizing sheaf on a proper scheme X of dimension n over a field k is a coherent sheaf \omega_X together with a linear functional that induces a natural isomorphism of vector spaces for each coherent sheaf F on X (the superscript * refers to a dual vector space).
New!!: Duality (mathematics) and Dualizing sheaf · See more »
Electric field
An electric field is a vector field surrounding an electric charge that exerts force on other charges, attracting or repelling them.
New!!: Duality (mathematics) and Electric field · See more »
Epimorphism
In category theory, an epimorphism (also called an epic morphism or, colloquially, an epi) is a morphism f: X → Y that is right-cancellative in the sense that, for all morphisms, Epimorphisms are categorical analogues of surjective functions (and in the category of sets the concept corresponds to the surjective functions), but it may not exactly coincide in all contexts; for example, the inclusion \mathbb\to\mathbb is a ring-epimorphism.
New!!: Duality (mathematics) and Epimorphism · See more »
Equivalence of categories
In category theory, an abstract branch of mathematics, an equivalence of categories is a relation between two categories that establishes that these categories are "essentially the same".
New!!: Duality (mathematics) and Equivalence of categories · See more »
Exterior algebra
In mathematics, the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogs.
New!!: Duality (mathematics) and Exterior algebra · See more »
Fibration
In topology, a branch of mathematics, a fibration is a generalization of the notion of a fiber bundle.
New!!: Duality (mathematics) and Fibration · See more »
Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
New!!: Duality (mathematics) and Field (mathematics) · See more »
Filter (mathematics)
In mathematics, a filter is a special subset of a partially ordered set.
New!!: Duality (mathematics) and Filter (mathematics) · See more »
Finite field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.
New!!: Duality (mathematics) and Finite field · See more »
Fixed point (mathematics)
In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is an element of the function's domain that is mapped to itself by the function.
New!!: Duality (mathematics) and Fixed point (mathematics) · See more »
Fourier analysis
In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions.
New!!: Duality (mathematics) and Fourier analysis · See more »
Fourier transform
The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.
New!!: Duality (mathematics) and Fourier transform · See more »
Function composition
In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.
New!!: Duality (mathematics) and Function composition · See more »
Function space
In mathematics, a function space is a set of functions between two fixed sets.
New!!: Duality (mathematics) and Function space · See more »
Functor
In mathematics, a functor is a map between categories.
New!!: Duality (mathematics) and Functor · See more »
Fundamental theorem of Galois theory
In mathematics, the fundamental theorem of Galois theory is a result that describes the structure of certain types of field extensions.
New!!: Duality (mathematics) and Fundamental theorem of Galois theory · See more »
G-module
In mathematics, given a group G, a G-module is an abelian group M on which G acts compatibly with the abelian group structure on M. This widely applicable notion generalizes that of a representation of ''G''.
New!!: Duality (mathematics) and G-module · See more »
Galois cohomology
In mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups.
New!!: Duality (mathematics) and Galois cohomology · See more »
Galois connection
In mathematics, especially in order theory, a Galois connection is a particular correspondence (typically) between two partially ordered sets (posets).
New!!: Duality (mathematics) and Galois connection · See more »
Galois extension
In mathematics, a Galois extension is an algebraic field extension E/F that is normal and separable; or equivalently, E/F is algebraic, and the field fixed by the automorphism group Aut(E/F) is precisely the base field F. The significance of being a Galois extension is that the extension has a Galois group and obeys the fundamental theorem of Galois theory.
New!!: Duality (mathematics) and Galois extension · See more »
Galois group
In mathematics, more specifically in the area of abstract algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension.
New!!: Duality (mathematics) and Galois group · See more »
Galois theory
In the field of algebra within mathematics, Galois theory, provides a connection between field theory and group theory.
New!!: Duality (mathematics) and Galois theory · See more »
Gelfand representation
In mathematics, the Gelfand representation in functional analysis (named after I. M. Gelfand) has two related meanings.
New!!: Duality (mathematics) and Gelfand representation · See more »
Geometric transformation
A geometric transformation is any bijection of a set having some geometric structure to itself or another such set.
New!!: Duality (mathematics) and Geometric transformation · See more »
Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
New!!: Duality (mathematics) and Geometry · See more »
Global field
In mathematics, a global field is a field that is either.
New!!: Duality (mathematics) and Global field · See more »
Graph embedding
In topological graph theory, an embedding (also spelled imbedding) of a graph G on a surface \Sigma is a representation of G on \Sigma in which points of \Sigma are associated with vertices and simple arcs (homeomorphic images of) are associated with edges in such a way that.
New!!: Duality (mathematics) and Graph embedding · See more »
Group cohomology
In mathematics (more specifically, in homological algebra), group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology.
New!!: Duality (mathematics) and Group cohomology · See more »
Group homomorphism
In mathematics, given two groups, (G, ∗) and (H, ·), a group homomorphism from (G, ∗) to (H, ·) is a function h: G → H such that for all u and v in G it holds that where the group operation on the left hand side of the equation is that of G and on the right hand side that of H. From this property, one can deduce that h maps the identity element eG of G to the identity element eH of H, and it also maps inverses to inverses in the sense that Hence one can say that h "is compatible with the group structure".
New!!: Duality (mathematics) and Group homomorphism · See more »
Half-space (geometry)
In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space.
New!!: Duality (mathematics) and Half-space (geometry) · See more »
Hamiltonian mechanics
Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics.
New!!: Duality (mathematics) and Hamiltonian mechanics · See more »
Hausdorff space
In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods.
New!!: Duality (mathematics) and Hausdorff space · See more »
Heyting algebra
In mathematics, a Heyting algebra is a bounded lattice (with join and meet operations written ∨ and ∧ and with least element 0 and greatest element 1) equipped with a binary operation a → b of implication such that c ∧ a ≤ b is equivalent to c ≤ a → b. From a logical standpoint, A → B is by this definition the weakest proposition for which modus ponens, the inference rule A → B, A ⊢ B, is sound.
New!!: Duality (mathematics) and Heyting algebra · See more »
Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
New!!: Duality (mathematics) and Hilbert space · See more »
Hodge star operator
In mathematics, the Hodge isomorphism or Hodge star operator is an important linear map introduced in general by W. V. D. Hodge.
New!!: Duality (mathematics) and Hodge star operator · See more »
Hom functor
In mathematics, specifically in category theory, hom-sets, i.e. sets of morphisms between objects, give rise to important functors to the category of sets.
New!!: Duality (mathematics) and Hom functor · See more »
Homological algebra
Homological algebra is the branch of mathematics that studies homology in a general algebraic setting.
New!!: Duality (mathematics) and Homological algebra · See more »
Homological mirror symmetry
Homological mirror symmetry is a mathematical conjecture made by Maxim Kontsevich.
New!!: Duality (mathematics) and Homological mirror symmetry · See more »
Homology (mathematics)
In mathematics, homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.
New!!: Duality (mathematics) and Homology (mathematics) · See more »
Hypoelliptic operator
In the theory of partial differential equations, a partial differential operator P defined on an open subset is called hypoelliptic if for every distribution u defined on an open subset V \subset U such that Pu is C^\infty (smooth), u must also be C^\infty.
New!!: Duality (mathematics) and Hypoelliptic operator · See more »
Ideal (order theory)
In mathematical order theory, an ideal is a special subset of a partially ordered set (poset).
New!!: Duality (mathematics) and Ideal (order theory) · See more »
If and only if
In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.
New!!: Duality (mathematics) and If and only if · See more »
Image functors for sheaves
In mathematics, especially in sheaf theory, a domain applied in areas such as topology, logic and algebraic geometry, there are four image functors for sheaves which belong together in various senses.
New!!: Duality (mathematics) and Image functors for sheaves · See more »
Injective module
In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z-module Q of all rational numbers.
New!!: Duality (mathematics) and Injective module · See more »
Inner product space
In linear algebra, an inner product space is a vector space with an additional structure called an inner product.
New!!: Duality (mathematics) and Inner product space · See more »
Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
New!!: Duality (mathematics) and Integer · See more »
Interior (topology)
In mathematics, specifically in topology, the interior of a subset S of points of a topological space X consists of all points of S that do not belong to the boundary of S. A point that is in the interior of S is an interior point of S. The interior of S is the complement of the closure of the complement of S. In this sense interior and closure are dual notions.
New!!: Duality (mathematics) and Interior (topology) · See more »
Intersection homology
In topology, a branch of mathematics, intersection homology is an analogue of singular homology especially well-suited for the study of singular spaces, discovered by Mark Goresky and Robert MacPherson in the fall of 1974 and developed by them over the next few years.
New!!: Duality (mathematics) and Intersection homology · See more »
Intersection number
In mathematics, and especially in algebraic geometry, the intersection number generalizes the intuitive notion of counting the number of times two curves intersect to higher dimensions, multiple (more than 2) curves, and accounting properly for tangency.
New!!: Duality (mathematics) and Intersection number · See more »
Involution (mathematics)
In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.
New!!: Duality (mathematics) and Involution (mathematics) · See more »
Isomorphism
In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.
New!!: Duality (mathematics) and Isomorphism · See more »
John Wiley & Sons
John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing.
New!!: Duality (mathematics) and John Wiley & Sons · See more »
Koszul duality
In mathematics, Koszul duality, named after the French mathematician Jean-Louis Koszul, is any of various kinds of dualities found in representation theory of Lie algebras, abstract algebras (semisimple algebra) as well as topology (e.g., equivariant cohomology).
New!!: Duality (mathematics) and Koszul duality · See more »
Kripke semantics
Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Joyal.
New!!: Duality (mathematics) and Kripke semantics · See more »
Lagrangian mechanics
Lagrangian mechanics is a reformulation of classical mechanics, introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in 1788.
New!!: Duality (mathematics) and Lagrangian mechanics · See more »
Langlands dual group
In representation theory, a branch of mathematics, the Langlands dual LG of a reductive algebraic group G (also called the L-group of G) is a group that controls the representation theory of G. If G is defined over a field k, then LG is an extension of the absolute Galois group of k by a complex Lie group.
New!!: Duality (mathematics) and Langlands dual group · See more »
Laplace transform
In mathematics, the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.
New!!: Duality (mathematics) and Laplace transform · See more »
Lattice (group)
In geometry and group theory, a lattice in \mathbbR^n is a subgroup of the additive group \mathbb^n which is isomorphic to the additive group \mathbbZ^n, and which spans the real vector space \mathbb^n.
New!!: Duality (mathematics) and Lattice (group) · See more »
Lebesgue integration
In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the -axis.
New!!: Duality (mathematics) and Lebesgue integration · See more »
Legendre transformation
In mathematics and physics, the Legendre transformation, named after Adrien-Marie Legendre, is an involutive transformation on the real-valued convex functions of one real variable.
New!!: Duality (mathematics) and Legendre transformation · See more »
Limit (category theory)
In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products, pullbacks and inverse limits.
New!!: Duality (mathematics) and Limit (category theory) · See more »
Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.
New!!: Duality (mathematics) and Linear algebra · See more »
Linear map
In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.
New!!: Duality (mathematics) and Linear map · See more »
Linear programming
Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.
New!!: Duality (mathematics) and Linear programming · See more »
Line–line intersection
In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or a line.
New!!: Duality (mathematics) and Line–line intersection · See more »
List of dualities
In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A.
New!!: Duality (mathematics) and List of dualities · See more »
Local field
In mathematics, a local field is a special type of field that is a locally compact topological field with respect to a non-discrete topology.
New!!: Duality (mathematics) and Local field · See more »
Local Tate duality
In Galois cohomology, local Tate duality (or simply local duality) is a duality for Galois modules for the absolute Galois group of a non-archimedean local field.
New!!: Duality (mathematics) and Local Tate duality · See more »
Locally compact space
In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space.
New!!: Duality (mathematics) and Locally compact space · See more »
Lp space
In mathematics, the Lp spaces are function spaces defined using a natural generalization of the ''p''-norm for finite-dimensional vector spaces.
New!!: Duality (mathematics) and Lp space · See more »
Magnetic field
A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials.
New!!: Duality (mathematics) and Magnetic field · See more »
Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
New!!: Duality (mathematics) and Manifold · See more »
Mathematical analysis
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
New!!: Duality (mathematics) and Mathematical analysis · See more »
Mathematical optimization
In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.
New!!: Duality (mathematics) and Mathematical optimization · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: Duality (mathematics) and Mathematics · See more »
Matlis duality
In algebra, Matlis duality is a duality between Artinian and Noetherian modules over a complete Noetherian local ring.
New!!: Duality (mathematics) and Matlis duality · See more »
Matroid
In combinatorics, a branch of mathematics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces.
New!!: Duality (mathematics) and Matroid · See more »
Maximal and minimal elements
In mathematics, especially in order theory, a maximal element of a subset S of some partially ordered set (poset) is an element of S that is not smaller than any other element in S. A minimal element of a subset S of some partially ordered set is defined dually as an element of S that is not greater than any other element in S. The notions of maximal and minimal elements are weaker than those of greatest element and least element which are also known, respectively, as maximum and minimum.
New!!: Duality (mathematics) and Maximal and minimal elements · See more »
Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
New!!: Duality (mathematics) and Maxwell's equations · See more »
Michael Atiyah
Sir Michael Francis Atiyah (born 22 April 1929) is an English mathematician specialising in geometry.
New!!: Duality (mathematics) and Michael Atiyah · See more »
Modal logic
Modal logic is a type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality.
New!!: Duality (mathematics) and Modal logic · See more »
Model category
In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak equivalences', 'fibrations' and 'cofibrations'.
New!!: Duality (mathematics) and Model category · See more »
Module (mathematics)
In mathematics, a module is one of the fundamental algebraic structures used in abstract algebra.
New!!: Duality (mathematics) and Module (mathematics) · See more »
Momentum
In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object.
New!!: Duality (mathematics) and Momentum · See more »
Monomorphism
In the context of abstract algebra or universal algebra, a monomorphism is an injective homomorphism.
New!!: Duality (mathematics) and Monomorphism · See more »
Negation
In logic, negation, also called the logical complement, is an operation that takes a proposition P to another proposition "not P", written \neg P (¬P), which is interpreted intuitively as being true when P is false, and false when P is true.
New!!: Duality (mathematics) and Negation · See more »
Noncommutative geometry
Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions (possibly in some generalized sense).
New!!: Duality (mathematics) and Noncommutative geometry · See more »
Open set
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
New!!: Duality (mathematics) and Open set · See more »
Opposite category
In category theory, a branch of mathematics, the opposite category or dual category Cop of a given category C is formed by reversing the morphisms, i.e. interchanging the source and target of each morphism.
New!!: Duality (mathematics) and Opposite category · See more »
Order isomorphism
In the mathematical field of order theory an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets (posets).
New!!: Duality (mathematics) and Order isomorphism · See more »
Orthogonality
In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.
New!!: Duality (mathematics) and Orthogonality · See more »
Pairing
In mathematics, a pairing is an R-bilinear map of modules, where R is the underlying ring.
New!!: Duality (mathematics) and Pairing · See more »
Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
New!!: Duality (mathematics) and Partial differential equation · See more »
Partially ordered set
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.
New!!: Duality (mathematics) and Partially ordered set · See more »
Planar graph
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.
New!!: Duality (mathematics) and Planar graph · See more »
Platonic solid
In three-dimensional space, a Platonic solid is a regular, convex polyhedron.
New!!: Duality (mathematics) and Platonic solid · See more »
Poincaré duality
In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds.
New!!: Duality (mathematics) and Poincaré duality · See more »
Pole and polar
In geometry, the pole and polar are respectively a point and a line that have a unique reciprocal relationship with respect to a given conic section.
New!!: Duality (mathematics) and Pole and polar · See more »
Pontryagin duality
In mathematics, specifically in harmonic analysis and the theory of topological groups, Pontryagin duality explains the general properties of the Fourier transform on locally compact abelian groups, such as \R, the circle, or finite cyclic groups.
New!!: Duality (mathematics) and Pontryagin duality · See more »
Positive definiteness
In mathematics, positive definiteness is a property of any object to which a bilinear form or a sesquilinear form may be naturally associated, which is positive definite.
New!!: Duality (mathematics) and Positive definiteness · See more »
Power set
In mathematics, the power set (or powerset) of any set is the set of all subsets of, including the empty set and itself, variously denoted as, 𝒫(), ℘() (using the "Weierstrass p"),,, or, identifying the powerset of with the set of all functions from to a given set of two elements,.
New!!: Duality (mathematics) and Power set · See more »
Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University.
New!!: Duality (mathematics) and Princeton University Press · See more »
Profinite group
In mathematics, profinite groups are topological groups that are in a certain sense assembled from finite groups.
New!!: Duality (mathematics) and Profinite group · See more »
Projective module
In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, by keeping some of the main properties of free modules.
New!!: Duality (mathematics) and Projective module · See more »
Projective plane
In mathematics, a projective plane is a geometric structure that extends the concept of a plane.
New!!: Duality (mathematics) and Projective plane · See more »
Projective variety
In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective ''n''-space Pn over k that is the zero-locus of some finite family of homogeneous polynomials of n + 1 variables with coefficients in k, that generate a prime ideal, the defining ideal of the variety.
New!!: Duality (mathematics) and Projective variety · See more »
Pullback (category theory)
In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit of a diagram consisting of two morphisms and with a common codomain.
New!!: Duality (mathematics) and Pullback (category theory) · See more »
Quantifier (logic)
In logic, quantification specifies the quantity of specimens in the domain of discourse that satisfy an open formula.
New!!: Duality (mathematics) and Quantifier (logic) · See more »
Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
New!!: Duality (mathematics) and Quantum mechanics · See more »
Quotient module
In algebra, given a module and a submodule, one can construct their quotient module.
New!!: Duality (mathematics) and Quotient module · See more »
Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
New!!: Duality (mathematics) and Real number · See more »
Reflexive space
In the area of mathematics known as functional analysis, a reflexive space is a Banach space (or more generally a locally convex topological vector space) that coincides with the continuous dual of its continuous dual space, both as linear space and as topological space.
New!!: Duality (mathematics) and Reflexive space · See more »
Riemannian geometry
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point that varies smoothly from point to point.
New!!: Duality (mathematics) and Riemannian geometry · See more »
Riemannian manifold
In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.
New!!: Duality (mathematics) and Riemannian manifold · See more »
Riesz representation theorem
There are several well-known theorems in functional analysis known as the Riesz representation theorem.
New!!: Duality (mathematics) and Riesz representation theorem · See more »
Ring homomorphism
In ring theory or abstract algebra, a ring homomorphism is a function between two rings which respects the structure.
New!!: Duality (mathematics) and Ring homomorphism · See more »
Ringed space
In mathematics, a ringed space can be equivalently thought of as either Ringed spaces appear in analysis as well as complex algebraic geometry and scheme theory of algebraic geometry.
New!!: Duality (mathematics) and Ringed space · See more »
S-duality
In theoretical physics, S-duality is an equivalence of two physical theories, which may be either quantum field theories or string theories.
New!!: Duality (mathematics) and S-duality · See more »
Scheme (mathematics)
In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x.
New!!: Duality (mathematics) and Scheme (mathematics) · See more »
Serre duality
In algebraic geometry, a branch of mathematics, Serre duality is a duality present on non-singular projective algebraic varieties V of dimension n (and in greater generality for vector bundles and further, for coherent sheaves).
New!!: Duality (mathematics) and Serre duality · See more »
Sheaf cohomology
In mathematics, sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space.
New!!: Duality (mathematics) and Sheaf cohomology · See more »
Singular homology
In algebraic topology, a branch of mathematics, singular homology refers to the study of a certain set of algebraic invariants of a topological space X, the so-called homology groups H_n(X).
New!!: Duality (mathematics) and Singular homology · See more »
Singular point of an algebraic variety
In the mathematical field of algebraic geometry, a singular point of an algebraic variety V is a point P that is 'special' (so, singular), in the geometric sense that at this point the tangent space at the variety may not be regularly defined.
New!!: Duality (mathematics) and Singular point of an algebraic variety · See more »
Sober space
In mathematics, a sober space is a topological space X such that every irreducible closed subset of X is the closure of exactly one point of X: that is, this closed subset has a unique generic point.
New!!: Duality (mathematics) and Sober space · See more »
Spectrum
A spectrum (plural spectra or spectrums) is a condition that is not limited to a specific set of values but can vary, without steps, across a continuum.
New!!: Duality (mathematics) and Spectrum · See more »
Spectrum of a ring
In abstract algebra and algebraic geometry, the spectrum of a commutative ring R, denoted by \operatorname(R), is the set of all prime ideals of R. It is commonly augmented with the Zariski topology and with a structure sheaf, turning it into a locally ringed space.
New!!: Duality (mathematics) and Spectrum of a ring · See more »
Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
New!!: Duality (mathematics) and Springer Science+Business Media · See more »
Stone duality
In mathematics, there is an ample supply of categorical dualities between certain categories of topological spaces and categories of partially ordered sets.
New!!: Duality (mathematics) and Stone duality · See more »
Subset
In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.
New!!: Duality (mathematics) and Subset · See more »
T-duality
In theoretical physics, T-duality is an equivalence of two physical theories, which may be either quantum field theories or string theories.
New!!: Duality (mathematics) and T-duality · See more »
Tangent space
In mathematics, the tangent space of a manifold facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector that gives the displacement of the one point from the other.
New!!: Duality (mathematics) and Tangent space · See more »
Tannaka–Krein duality
In mathematics, Tannaka–Krein duality theory concerns the interaction of a compact topological group and its category of linear representations.
New!!: Duality (mathematics) and Tannaka–Krein duality · See more »
Temporal logic
In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time.
New!!: Duality (mathematics) and Temporal logic · See more »
The Princeton Companion to Mathematics
The Princeton Companion to Mathematics is a book, edited by Timothy Gowers with associate editors June Barrow-Green and Imre Leader, and published in 2008 by Princeton University Press.
New!!: Duality (mathematics) and The Princeton Companion to Mathematics · See more »
Topological group
In mathematics, a topological group is a group G together with a topology on G such that the group's binary operation and the group's inverse function are continuous functions with respect to the topology.
New!!: Duality (mathematics) and Topological group · See more »
Topological vector space
In mathematics, a topological vector space (also called a linear topological space) is one of the basic structures investigated in functional analysis.
New!!: Duality (mathematics) and Topological vector space · See more »
Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
New!!: Duality (mathematics) and Topology · See more »
Toric variety
In algebraic geometry, a toric variety or torus embedding is an algebraic variety containing an algebraic torus as an open dense subset, such that the action of the torus on itself extends to the whole variety.
New!!: Duality (mathematics) and Toric variety · See more »
Upper and lower bounds
In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set (K, ≤) is an element of K which is greater than or equal to every element of S. The term lower bound is defined dually as an element of K which is less than or equal to every element of S. A set with an upper bound is said to be bounded from above by that bound, a set with a lower bound is said to be bounded from below by that bound.
New!!: Duality (mathematics) and Upper and lower bounds · See more »
Upper set
In mathematics, an upper set (also called an upward closed set or just an upset) of a partially ordered set (X,≤) is a subset U with the property that, if x is in U and x≤y, then y is in U. The dual notion is lower set (alternatively, down set, decreasing set, initial segment, semi-ideal; the set is downward closed), which is a subset L with the property that, if x is in L and y≤x, then y is in L. The terms order ideal or ideal are sometimes used as synonyms for lower set.
New!!: Duality (mathematics) and Upper set · See more »
Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
New!!: Duality (mathematics) and Vector space · See more »
Velocity
The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.
New!!: Duality (mathematics) and Velocity · See more »
Verdier duality
In mathematics, Verdier duality is a duality in sheaf theory that generalizes Poincaré duality for manifolds.
New!!: Duality (mathematics) and Verdier duality · See more »
Vertex (geometry)
In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.
New!!: Duality (mathematics) and Vertex (geometry) · See more »
Voronoi diagram
In mathematics, a Voronoi diagram is a partitioning of a plane into regions based on distance to points in a specific subset of the plane.
New!!: Duality (mathematics) and Voronoi diagram · See more »
Redirects here:
Dual (math), Dual (mathematics), Dual (maths), Duality (math), Duality (maths), Duality in mathematics, Duality theorem, Duality theory, Mathematical duality, Self-dual, Selfdual.
References
[1] https://en.wikipedia.org/wiki/Duality_(mathematics)
