Faster access than browser!
92 relations: Abelian group, Absorbing set, Academic Press, Algebra, Balanced set, Banach space, Banach–Alaoglu theorem, Barrelled space, Bornological space, Bounded operator, Bounded set (topological vector space), Cambridge University Press, Cartesian product, Category (mathematics), Cauchy sequence, Closed graph theorem, Closed set, Compact space, Complete metric space, Complex number, Continuous function, Continuous linear operator, Convex set, Countable set, Dense set, Dimension (vector space), Distribution (mathematics), Dual space, Equivalence of metrics, Euclidean space, F-space, Field extension, Fréchet space, Function (mathematics), Functional analysis, Graduate Texts in Mathematics, Hahn–Banach theorem, Hausdorff space, Hilbert space, Holomorphic function, Hyperplane, Inner product space, Inverse limit, Kernel (algebra), LF-space, Limit (category theory), Limit of a sequence, Linear form, Linear map, Linear subspace, ..., Locally compact space, Locally convex topological vector space, Lp space, Mathematics, Metric (mathematics), Metric space, Metrization theorem, Minkowski functional, Montel space, Morphism, Neighbourhood system, Norm (mathematics), Normed vector space, Nuclear operator, Nuclear space, Open mapping theorem (functional analysis), Pointwise convergence, Product topology, Quotient space (topology), Real number, Reflexive space, S&P Global, Schwartz space, Smoothness, Springer Science+Business Media, Stereotype space, Subspace topology, T1 space, Topological group, Topological ring, Topological space, Topology, Totally bounded space, Triangle inequality, Tychonoff space, Uniform boundedness principle, Uniform continuity, Uniform convergence, Uniform space, Vector space, Walter Rudin, Weak topology. Expand index (42 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!!: Topological vector space and Abelian group · See more »
Absorbing set
In functional analysis and related areas of mathematics an absorbing set in a vector space is a set S which can be inflated to include any element of the vector space.
New!!: Topological vector space and Absorbing set · See more »
Academic Press
Academic Press is an academic book publisher.
New!!: Topological vector space and Academic Press · See more »
Algebra
Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.
New!!: Topological vector space and Algebra · See more »
Balanced set
In linear algebra and related areas of mathematics a balanced set, circled set or disk in a vector space (over a field K with an absolute value function |\cdot |) is a set S such that for all scalars \alpha with |\alpha| \leqslant 1 where The balanced hull or balanced envelope for a set S is the smallest balanced set containing S. It can be constructed as the intersection of all balanced sets containing S.
New!!: Topological vector space and Balanced set · See more »
Banach space
In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.
New!!: Topological vector space and Banach space · See more »
Banach–Alaoglu theorem
In functional analysis and related branches of mathematics, the Banach–Alaoglu theorem (also known as Alaoglu's theorem) states that the closed unit ball of the dual space of a normed vector space is compact in the weak* topology.
New!!: Topological vector space and Banach–Alaoglu theorem · See more »
Barrelled space
In functional analysis and related areas of mathematics, barrelled spaces are Hausdorff topological vector spaces for which every barrelled set in the space is a neighbourhood for the zero vector.
New!!: Topological vector space and Barrelled space · See more »
Bornological space
In mathematics, particularly in functional analysis, a bornological space is a type of space which, in some sense, possesses the minimum amount of structure needed to address questions of boundedness of sets and functions, in the same way that a topological space possesses the minimum amount of structure needed to address questions of continuity.
New!!: Topological vector space and Bornological space · See more »
Bounded operator
In functional analysis, a bounded linear operator is a linear transformation L between normed vector spaces X and Y for which the ratio of the norm of L(v) to that of v is bounded above by the same number, over all non-zero vectors v in X. In other words, there exists some M\ge 0 such that for all v in X The smallest such M is called the operator norm \|L\|_ \, of L. A bounded linear operator is generally not a bounded function; the latter would require that the norm of L(v) be bounded for all v, which is not possible unless L(v).
New!!: Topological vector space and Bounded operator · See more »
Bounded set (topological vector space)
In functional analysis and related areas of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to include the set.
New!!: Topological vector space and Bounded set (topological vector space) · See more »
Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
New!!: Topological vector space 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!!: Topological vector space and Cartesian product · 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!!: Topological vector space and Category (mathematics) · See more »
Cauchy sequence
In mathematics, a Cauchy sequence, named after Augustin-Louis Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses.
New!!: Topological vector space and Cauchy sequence · See more »
Closed graph theorem
In mathematics, the closed graph theorem is a basic result which characterizes continuous functions in terms of their graphs.
New!!: Topological vector space and Closed graph theorem · 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!!: Topological vector space and Closed set · 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!!: Topological vector space and Compact space · See more »
Complete metric space
In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in M converges in M. Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary).
New!!: Topological vector space and Complete metric space · 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!!: Topological vector space and Complex number · See more »
Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
New!!: Topological vector space and Continuous function · See more »
Continuous linear operator
In functional analysis and related areas of mathematics, a continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector spaces.
New!!: Topological vector space and Continuous linear operator · See more »
Convex set
In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.
New!!: Topological vector space and Convex set · See more »
Countable set
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
New!!: Topological vector space and Countable set · See more »
Dense set
In topology and related areas of mathematics, a subset A of a topological space X is called dense (in X) if every point x in X either belongs to A or is a limit point of A, that is the closure of A is constituting the whole set X. Informally, for every point in X, the point is either in A or arbitrarily "close" to a member of A — for instance, every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation).
New!!: Topological vector space and Dense set · 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!!: Topological vector space and Dimension (vector space) · See more »
Distribution (mathematics)
Distributions (or generalized functions) are objects that generalize the classical notion of functions in mathematical analysis.
New!!: Topological vector space and Distribution (mathematics) · 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!!: Topological vector space and Dual space · See more »
Equivalence of metrics
In the study of metric spaces in mathematics, there are various notions of two metrics on the same underlying space being "the same", or equivalent.
New!!: Topological vector space and Equivalence of metrics · See more »
Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
New!!: Topological vector space and Euclidean space · See more »
F-space
In functional analysis, an F-space is a vector space V over the real or complex numbers together with a metric d: V × V → R so that.
New!!: Topological vector space and F-space · See more »
Field extension
In mathematics, and in particular, algebra, a field E is an extension field of a field F if E contains F and the operations of F are those of E restricted to F. Equivalently, F is a subfield of E. For example, under the usual notions of addition and multiplication, the complex numbers are an extension field of the real numbers; the real numbers are a subfield of the complex numbers.
New!!: Topological vector space and Field extension · See more »
Fréchet space
In functional analysis and related areas of mathematics, Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces.
New!!: Topological vector space and Fréchet space · See more »
Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
New!!: Topological vector space and Function (mathematics) · See more »
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense.
New!!: Topological vector space and Functional analysis · See more »
Graduate Texts in Mathematics
Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.
New!!: Topological vector space and Graduate Texts in Mathematics · See more »
Hahn–Banach theorem
In mathematics, the Hahn–Banach theorem is a central tool in functional analysis.
New!!: Topological vector space and Hahn–Banach theorem · 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!!: Topological vector space and Hausdorff space · See more »
Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
New!!: Topological vector space and Hilbert space · See more »
Holomorphic function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.
New!!: Topological vector space and Holomorphic function · See more »
Hyperplane
In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.
New!!: Topological vector space and Hyperplane · 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!!: Topological vector space and Inner product space · See more »
Inverse limit
In mathematics, the inverse limit (also called the projective limit or limit) is a construction that allows one to "glue together" several related objects, the precise manner of the gluing process being specified by morphisms between the objects.
New!!: Topological vector space and Inverse limit · See more »
Kernel (algebra)
In the various branches of mathematics that fall under the heading of abstract algebra, the kernel of a homomorphism measures the degree to which the homomorphism fails to be injective.
New!!: Topological vector space and Kernel (algebra) · See more »
LF-space
In mathematics, an LF-space is a topological vector space V that is a locally convex inductive limit of a countable inductive system (V_n, i_) of Fréchet spaces.
New!!: Topological vector space and LF-space · 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!!: Topological vector space and Limit (category theory) · See more »
Limit of a sequence
As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.
New!!: Topological vector space and Limit of a sequence · See more »
Linear form
In linear algebra, a linear functional or linear form (also called a one-form or covector) is a linear map from a vector space to its field of scalars.
New!!: Topological vector space and Linear form · 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!!: Topological vector space and Linear map · See more »
Linear subspace
In linear algebra and related fields of mathematics, a linear subspace, also known as a vector subspace, or, in the older literature, a linear manifold, is a vector space that is a subset of some other (higher-dimension) vector space.
New!!: Topological vector space and Linear subspace · 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!!: Topological vector space and Locally compact space · See more »
Locally convex topological vector space
In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces.
New!!: Topological vector space and Locally convex topological vector 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!!: Topological vector space and Lp space · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: Topological vector space and Mathematics · See more »
Metric (mathematics)
In mathematics, a metric or distance function is a function that defines a distance between each pair of elements of a set.
New!!: Topological vector space and Metric (mathematics) · See more »
Metric space
In mathematics, a metric space is a set for which distances between all members of the set are defined.
New!!: Topological vector space and Metric space · See more »
Metrization theorem
In topology and related areas of mathematics, a metrizable space is a topological space that is homeomorphic to a metric space.
New!!: Topological vector space and Metrization theorem · See more »
Minkowski functional
In mathematics, in the field of functional analysis, a Minkowski functional is a function that recovers a notion of distance on a linear space.
New!!: Topological vector space and Minkowski functional · See more »
Montel space
In functional analysis and related areas of mathematics, a Montel space, named after Paul Montel, is any topological vector space in which an analog of Montel's theorem holds.
New!!: Topological vector space and Montel space · See more »
Morphism
In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.
New!!: Topological vector space and Morphism · See more »
Neighbourhood system
In topology and related areas of mathematics, the neighbourhood system, complete system of neighbourhoods, or neighbourhood filter \mathcal(x) for a point x is the collection of all neighbourhoods for the point x.
New!!: Topological vector space and Neighbourhood system · See more »
Norm (mathematics)
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.
New!!: Topological vector space and Norm (mathematics) · See more »
Normed vector space
In mathematics, a normed vector space is a vector space over the real or complex numbers, on which a norm is defined.
New!!: Topological vector space and Normed vector space · See more »
Nuclear operator
In mathematics, a nuclear operator is a compact operator for which a trace may be defined, such that the trace is finite and independent of the choice of basis (at least on well behaved spaces; there are some spaces on which nuclear operators do not have a trace).
New!!: Topological vector space and Nuclear operator · See more »
Nuclear space
In mathematics, a nuclear space is a topological vector space with many of the good properties of finite-dimensional vector spaces.
New!!: Topological vector space and Nuclear space · See more »
Open mapping theorem (functional analysis)
In functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem (named after Stefan Banach and Juliusz Schauder), is a fundamental result which states that if a continuous linear operator between Banach spaces is surjective then it is an open map.
New!!: Topological vector space and Open mapping theorem (functional analysis) · See more »
Pointwise convergence
In mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function.
New!!: Topological vector space and Pointwise convergence · See more »
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.
New!!: Topological vector space and Product topology · See more »
Quotient space (topology)
In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or "gluing together" certain points of a given topological space.
New!!: Topological vector space and Quotient space (topology) · 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!!: Topological vector space 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!!: Topological vector space and Reflexive space · See more »
S&P Global
S&P Global Inc. (prior to April 2016 McGraw Hill Financial, Inc., and prior to 2013 McGraw Hill Companies) is an American publicly traded corporation headquartered in New York City.
New!!: Topological vector space and S&P Global · See more »
Schwartz space
In mathematics, Schwartz space is the function space of all functions whose derivatives are rapidly decreasing (defined rigorously below).
New!!: Topological vector space and Schwartz space · See more »
Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
New!!: Topological vector space and Smoothness · 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!!: Topological vector space and Springer Science+Business Media · See more »
Stereotype space
In functional analysis and related areas of mathematics, stereotype spaces are topological vector spaces defined by a special variant of reflexivity condition.
New!!: Topological vector space and Stereotype space · See more »
Subspace topology
In topology and related areas of mathematics, a subspace of a topological space X is a subset S of X which is equipped with a topology induced from that of X called the subspace topology (or the relative topology, or the induced topology, or the trace topology).
New!!: Topological vector space and Subspace topology · See more »
T1 space
In topology and related branches of mathematics, a T1 space is a topological space in which, for every pair of distinct points, each has a neighborhood not containing the other.
New!!: Topological vector space and T1 space · 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!!: Topological vector space and Topological group · See more »
Topological ring
In mathematics, a topological ring is a ring R which is also a topological space such that both the addition and the multiplication are continuous as maps where R × R carries the product topology.
New!!: Topological vector space and Topological ring · See more »
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.
New!!: Topological vector space and Topological 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!!: Topological vector space and Topology · See more »
Totally bounded space
In topology and related branches of mathematics, a totally bounded space is a space that can be covered by finitely many subsets of every fixed "size" (where the meaning of "size" depends on the given context).
New!!: Topological vector space and Totally bounded space · See more »
Triangle inequality
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
New!!: Topological vector space and Triangle inequality · See more »
Tychonoff space
In topology and related branches of mathematics, Tychonoff spaces and completely regular spaces are kinds of topological spaces.
New!!: Topological vector space and Tychonoff space · See more »
Uniform boundedness principle
In mathematics, the uniform boundedness principle or Banach–Steinhaus theorem is one of the fundamental results in functional analysis.
New!!: Topological vector space and Uniform boundedness principle · See more »
Uniform continuity
In mathematics, a function f is uniformly continuous if, roughly speaking, it is possible to guarantee that f(x) and f(y) be as close to each other as we please by requiring only that x and y are sufficiently close to each other; unlike ordinary continuity, the maximum distance between f(x) and f(y) cannot depend on x and y themselves.
New!!: Topological vector space and Uniform continuity · See more »
Uniform convergence
In the mathematical field of analysis, uniform convergence is a type of convergence of functions stronger than pointwise convergence.
New!!: Topological vector space and Uniform convergence · See more »
Uniform space
In the mathematical field of topology, a uniform space is a set with a uniform structure.
New!!: Topological vector space and Uniform space · 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!!: Topological vector space and Vector space · See more »
Walter Rudin
Walter Rudin (May 2, 1921 – May 20, 2010) was an Austrian-American mathematician and professor of Mathematics at the University of Wisconsin–Madison.
New!!: Topological vector space and Walter Rudin · See more »
Weak topology
In mathematics, weak topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators, for instance on a Hilbert space.
New!!: Topological vector space and Weak topology · See more »
Redirects here:
Linear topological space, Topological Vector Space, Topological linear spaces, Topological vector spaces.
References
[1] https://en.wikipedia.org/wiki/Topological_vector_space
