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131 relations: Adidas Telstar, Algebraic geometry, Algebraic topology, Algebraic variety, Angular defect, Antipodal point, Arthur Cayley, Augustin-Louis Cauchy, Ball (association football), Ball (mathematics), Betti number, Cardinality, Category (mathematics), Chain complex, Characteristic class, Chi (letter), Circle, Closed manifold, Coherent sheaf, Combinatorics, Compact space, Complement (set theory), Complex number, Connected space, Connected sum, Contractible space, Convex polytope, Counterexample, Covering space, Cube, Cubohemioctahedron, CW complex, Cycle (graph theory), David Eppstein, Density (polytope), Disjoint union, Dodecahedron, Edge (geometry), Euclidean space, Euler calculus, Euler characteristic of an orbifold, Euler class, Face (geometry), Fibration, Fullerene, Fundamental class, Genus (mathematics), Genus-three surface, Genus-two surface, Graph (discrete mathematics), ..., Great icosahedron, Greek alphabet, Group (mathematics), Group isomorphism, Groupoid, Hadwiger's theorem, Hexahedron, Homological algebra, Homology (mathematics), Homotopy, Icosahedron, Imre Lakatos, Incidence algebra, Inclusion–exclusion principle, Interior (topology), Interval (mathematics), John Milnor, Jordan curve theorem, Kepler–Poinsot polyhedron, Klein bottle, Leonhard Euler, Lie group, List of things named after Leonhard Euler, List of uniform polyhedra, Locally compact space, Mathematics, Möbius function, Möbius strip, Monoid, Octahedron, Octahemioctahedron, Orbifold, Orientability, Parallelizable manifold, Partially ordered set, Planar graph, Platonic solid, Poincaré duality, Polyhedral combinatorics, Polyhedron, Presses polytechniques et universitaires romandes, Product topology, Projective polyhedron, Projective space, Proofs and Refutations, Ramification (mathematics), Rank of an abelian group, Real line, Real projective plane, René Descartes, Riemann–Hurwitz formula, Riemannian manifold, Scalar multiplication, Scheme (mathematics), Serre spectral sequence, Set (mathematics), Sheaf cohomology, Shelling (topology), Shriek map, Simplicial complex, Singular homology, Sphere, Spherical polyhedron, Stereographic projection, Subset, Support (mathematics), Surface (topology), Tangent bundle, Tetrahedron, Tetrahemihexahedron, Topological property, Topological space, Topologically stratified space, Toroidal polyhedron, Torus, Union (set theory), Unit disk, Up to, Vector bundle, Vertex (geometry), Vertex figure. Expand index (81 more) »
Adidas Telstar
Telstar was a football made by Adidas.
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Algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
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Algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.
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Algebraic variety
Algebraic varieties are the central objects of study in algebraic geometry.
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Angular defect
In geometry, the (angular) defect (or deficit or deficiency) means the failure of some angles to add up to the expected amount of 360° or 180°, when such angles in the Euclidean plane would.
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Antipodal point
In mathematics, the antipodal point of a point on the surface of a sphere is the point which is diametrically opposite to it — so situated that a line drawn from the one to the other passes through the center of the sphere and forms a true diameter.
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Arthur Cayley
Arthur Cayley F.R.S. (16 August 1821 – 26 January 1895) was a British mathematician.
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Augustin-Louis Cauchy
Baron Augustin-Louis Cauchy FRS FRSE (21 August 178923 May 1857) was a French mathematician, engineer and physicist who made pioneering contributions to several branches of mathematics, including: mathematical analysis and continuum mechanics.
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Ball (association football)
A football, soccer ball, or association football ball is the ball used in the sport of association football.
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Ball (mathematics)
In mathematics, a ball is the space bounded by a sphere.
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Betti number
In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of n-dimensional simplicial complexes.
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Cardinality
In mathematics, the cardinality of a set is a measure of the "number of elements of the set".
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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.
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Chain complex
In mathematics, a chain complex is an algebraic structure that consists of a sequence of abelian groups (or modules) and a sequence of homomorphisms between consecutive groups such that the image of each homomorphism is included in the kernel of the next.
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Characteristic class
In mathematics, a characteristic class is a way of associating to each principal bundle X a cohomology class of X. The cohomology class measures the extent the bundle is "twisted" — and whether it possesses sections.
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Chi (letter)
Chi (uppercase Χ, lowercase χ; χῖ) is the 22nd letter of the Greek alphabet, pronounced or in English.
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Circle
A circle is a simple closed shape.
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Closed manifold
In mathematics, a closed manifold is a type of topological space, namely a compact manifold without boundary.
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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.
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Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.
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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).
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Complement (set theory)
In set theory, the complement of a set refers to elements not in.
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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.
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Connected space
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets.
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Connected sum
In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds.
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Contractible space
In mathematics, a topological space X is contractible if the identity map on X is null-homotopic, i.e. if it is homotopic to some constant map.
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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.
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Counterexample
In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule or law.
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Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.
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Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
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Cubohemioctahedron
In geometry, the cubohemioctahedron is a nonconvex uniform polyhedron, indexed as U15.
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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.
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Cycle (graph theory)
In graph theory, a cycle is a path of edges and vertices wherein a vertex is reachable from itself.
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David Eppstein
David Arthur Eppstein (born 1963) is an American computer scientist and mathematician.
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Density (polytope)
In geometry, the density of a polytope represents the number of windings of a polytope, particularly a uniform or regular polytope, around its center.
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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.
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Dodecahedron
In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.
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Edge (geometry)
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.
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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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Euler calculus
Euler calculus is a methodology from applied algebraic topology and integral geometry that integrates constructible functions and more recently definable functions by integrating with respect to the Euler characteristic as a finitely-additive measure.
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Euler characteristic of an orbifold
In differential geometry, the Euler characteristic of an orbifold, or orbifold Euler characteristic, is a generalization of the topological Euler characteristic that includes contributions coming from nontrivial automorphisms.
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Euler class
In mathematics, specifically in algebraic topology, the Euler class is a characteristic class of oriented, real vector bundles.
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Face (geometry)
In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.
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Fibration
In topology, a branch of mathematics, a fibration is a generalization of the notion of a fiber bundle.
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Fullerene
A fullerene is a molecule of carbon in the form of a hollow sphere, ellipsoid, tube, and many other shapes.
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Fundamental class
In mathematics, the fundamental class is a homology class associated to an oriented manifold M of dimension n, which corresponds to the generator of the homology group H_n(M;\mathbf)\cong\mathbf.
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Genus (mathematics)
In mathematics, genus (plural genera) has a few different, but closely related, meanings.
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Genus-three surface
In geometry, a genus-three surface is a smooth closed surface with three holes, or, in other words, a surface of genus three.
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Genus-two surface
In mathematics, a genus-two surface (also known as a double torus or two-holed torus) is a surface formed by the connected sum of two tori.
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Graph (discrete mathematics)
In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
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Great icosahedron
In geometry, the great icosahedron is one of four Kepler-Poinsot polyhedra (nonconvex regular polyhedra), with Schläfli symbol and Coxeter-Dynkin diagram of.
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Greek alphabet
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC.
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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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Group isomorphism
In abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the given group operations.
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Groupoid
In mathematics, especially in category theory and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of group in several equivalent ways.
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Hadwiger's theorem
In integral geometry (otherwise called geometric probability theory), Hadwiger's theorem characterises the valuations on convex bodies in Rn.
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Hexahedron
A hexahedron (plural: hexahedra) is any polyhedron with six faces.
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Homological algebra
Homological algebra is the branch of mathematics that studies homology in a general algebraic setting.
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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.
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Homotopy
In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.
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Icosahedron
In geometry, an icosahedron is a polyhedron with 20 faces.
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Imre Lakatos
Imre Lakatos (Lakatos Imre; November 9, 1922 – February 2, 1974) was a Hungarian philosopher of mathematics and science, known for his thesis of the fallibility of mathematics and its 'methodology of proofs and refutations' in its pre-axiomatic stages of development, and also for introducing the concept of the 'research programme' in his methodology of scientific research programmes.
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Incidence algebra
In order theory, a field of mathematics, an incidence algebra is an associative algebra, defined for every locally finite partially ordered set and commutative ring with unity.
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Inclusion–exclusion principle
In combinatorics (combinatorial mathematics), the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as where A and B are two finite sets and |S| indicates the cardinality of a set S (which may be considered as the number of elements of the set, if the set is finite).
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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.
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Interval (mathematics)
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
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John Milnor
John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, K-theory and dynamical systems.
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Jordan curve theorem
In topology, a Jordan curve, sometimes called a plane simple closed curve, is a non-self-intersecting continuous loop in the plane.
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Kepler–Poinsot polyhedron
In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.
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Klein bottle
In topology, a branch of mathematics, the Klein bottle is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined.
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Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
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Lie group
In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.
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List of things named after Leonhard Euler
Leonhard Euler (1707–1783)In mathematics and physics, there are a large number of topics named in honor of Swiss mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations.
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List of uniform polyhedra
In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other).
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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.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Möbius function
The classical Möbius function is an important multiplicative function in number theory and combinatorics.
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Möbius strip
The Möbius strip or Möbius band, also spelled Mobius or Moebius, is a surface with only one side (when embedded in three-dimensional Euclidean space) and only one boundary.
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Monoid
In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element.
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Octahedron
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.
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Octahemioctahedron
In geometry, the octahemioctahedron or allelotetratetrahedron is a nonconvex uniform polyhedron, indexed as U3.
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Orbifold
In the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold (for "orbit-manifold") is a generalization of a manifold.
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Orientability
In mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point.
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Parallelizable manifold
In mathematics, a differentiable manifold M of dimension n is called parallelizable if there exist smooth vector fields on the manifold, such that at any point p of M the tangent vectors provide a basis of the tangent space at p. Equivalently, the tangent bundle is a trivial bundle, so that the associated principal bundle of linear frames has a section on M. A particular choice of such a basis of vector fields on M is called a parallelization (or an absolute parallelism) of M.
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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.
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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.
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Platonic solid
In three-dimensional space, a Platonic solid is a regular, convex polyhedron.
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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.
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Polyhedral combinatorics
Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes.
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Polyhedron
In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.
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Presses polytechniques et universitaires romandes
The Presses polytechniques et universitaires romandes (PPUR, literally "Polytechnic and university press of French-speaking Switzerland") is a Swiss academic publishing house.
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Product topology
In topology and related areas of mathematics, a product space is the cartesian product of a family of topological spaces equipped with a natural topology called the product topology.
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Projective polyhedron
In geometry, a (globally) projective polyhedron is a tessellation of the real projective plane.
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Projective space
In mathematics, a projective space can be thought of as the set of lines through the origin of a vector space V. The cases when and are the real projective line and the real projective plane, respectively, where R denotes the field of real numbers, R2 denotes ordered pairs of real numbers, and R3 denotes ordered triplets of real numbers.
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Proofs and Refutations
Proofs and Refutations is a 1976 book by philosopher Imre Lakatos expounding his view of the progress of mathematics.
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Ramification (mathematics)
In geometry, ramification is 'branching out', in the way that the square root function, for complex numbers, can be seen to have two branches differing in sign.
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Rank of an abelian group
In mathematics, the rank, Prüfer rank, or torsion-free rank of an abelian group A is the cardinality of a maximal linearly independent subset.
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Real line
In mathematics, the real line, or real number line is the line whose points are the real numbers.
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Real projective plane
In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface.
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René Descartes
René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.
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Riemann–Hurwitz formula
In mathematics, the Riemann–Hurwitz formula, named after Bernhard Riemann and Adolf Hurwitz, describes the relationship of the Euler characteristics of two surfaces when one is a ramified covering of the other.
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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.
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Scalar multiplication
In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra).
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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.
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Serre spectral sequence
In mathematics, the Serre spectral sequence (sometimes Leray-Serre spectral sequence to acknowledge earlier work of Jean Leray in the Leray spectral sequence) is an important tool in algebraic topology.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Sheaf cohomology
In mathematics, sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space.
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Shelling (topology)
In mathematics, a shelling of a simplicial complex is a way of gluing it together from its maximal simplices (simplices that are not a face of another simplex) in a well-behaved way.
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Shriek map
In category theory, a branch of mathematics, certain unusual functors are denoted f_! and f^!, with the exclamation mark used to indicate that they are exceptional in some way.
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Simplicial complex
In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their ''n''-dimensional counterparts (see illustration).
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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).
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Sphere
A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
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Spherical polyhedron
In mathematics, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons.
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Stereographic projection
In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.
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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.
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Support (mathematics)
In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero.
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Surface (topology)
In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.
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Tangent bundle
In differential geometry, the tangent bundle of a differentiable manifold M is a manifold TM which assembles all the tangent vectors in M. As a set, it is given by the disjoint unionThe disjoint union ensures that for any two points x1 and x2 of manifold M the tangent spaces T1 and T2 have no common vector.
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Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.
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Tetrahemihexahedron
In geometry, the tetrahemihexahedron or hemicuboctahedron is a uniform star polyhedron, indexed as U4.
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Topological property
In topology and related areas of mathematics a topological property or topological invariant is a property of a topological space which is invariant under homeomorphisms.
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Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
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Topologically stratified space
In topology, a branch of mathematics, a topologically stratified space is a space X that has been decomposed into pieces called strata; these strata are topological manifolds and are required to fit together in a certain way.
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Toroidal polyhedron
In geometry, a toroidal polyhedron is a polyhedron which is also a toroid (a g-holed torus), having a topological genus of 1 or greater.
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Torus
In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.
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Union (set theory)
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.
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Unit disk
In mathematics, the open unit disk (or disc) around P (where P is a given point in the plane), is the set of points whose distance from P is less than 1: The closed unit disk around P is the set of points whose distance from P is less than or equal to one: Unit disks are special cases of disks and unit balls; as such, they contain the interior of the unit circle and, in the case of the closed unit disk, the unit circle itself.
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Up to
In mathematics, the phrase up to appears in discussions about the elements of a set (say S), and the conditions under which subsets of those elements may be considered equivalent.
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Vector bundle
In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to every point x of the space X we associate (or "attach") a vector space V(x) in such a way that these vector spaces fit together to form another space of the same kind as X (e.g. a topological space, manifold, or algebraic variety), which is then called a vector bundle over X.
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Vertex (geometry)
In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.
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Vertex figure
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
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Euler Characteristic, Euler number (topology), Euler polyhedron theorem, Euler's characteristic, Euler's formula for polyhedra, Euler's polyhedral formula, Euler's polyhedron formula, Euler's polyhedron theorem, Euler-Poincare characteristic, Euler-Poincaré characteristic, Euler–Poincaré characteristic, Polyhedral formula, Polyhedron formula, String theory Euler number.
References
[1] https://en.wikipedia.org/wiki/Euler_characteristic
