Table of Contents
28 relations: Alexander Grothendieck, Annales de l'Institut Fourier, Banach space, Barrelled space, Bornological space, Closure (topology), Dual system, Fréchet space, Functional analysis, H-space, Hausdorff space, Infrabarrelled space, LF-space, Locally convex topological vector space, Lp space, Mackey space, Mathematics, Metrizable space, Metrizable topological vector space, Montel space, Normed vector space, Polar set, Reflexive space, Semi-reflexive space, Separable space, Strong dual space, Topological vector space, Weak topology.
Alexander Grothendieck
Alexander Grothendieck (28 March 1928 – 13 November 2014) was a German-born mathematician who became the leading figure in the creation of modern algebraic geometry.
See Distinguished space and Alexander Grothendieck
Annales de l'Institut Fourier
The Annales de l'Institut Fourier is a French mathematical journal publishing papers in all fields of mathematics.
See Distinguished space and Annales de l'Institut Fourier
Banach space
In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space. Distinguished space and Banach space are topological vector spaces.
See Distinguished space and Banach space
Barrelled space
In functional analysis and related areas of mathematics, a barrelled space (also written barreled space) is a topological vector space (TVS) for which every barrelled set in the space is a neighbourhood for the zero vector. Distinguished space and barrelled space are topological vector spaces.
See Distinguished space and Barrelled space
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 linear maps, in the same way that a topological space possesses the minimum amount of structure needed to address questions of continuity. Distinguished space and bornological space are topological vector spaces.
See Distinguished space and Bornological space
Closure (topology)
In topology, the closure of a subset of points in a topological space consists of all points in together with all limit points of.
See Distinguished space and Closure (topology)
Dual system
In mathematics, a dual system, dual pair or a duality over a field \mathbb is a triple (X, Y, b) consisting of two vector spaces, X and Y, over \mathbb and a non-degenerate bilinear map b: X \times Y \to \mathbb. Distinguished space and dual system are topological vector spaces.
See Distinguished space and Dual system
Fréchet space
In functional analysis and related areas of mathematics, Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces. Distinguished space and Fréchet space are topological vector spaces.
See Distinguished space and Fréchet space
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 (for example, inner product, norm, or topology) and the linear functions defined on these spaces and suitably respecting these structures.
See Distinguished space and Functional analysis
H-space
In mathematics, an H-space is a homotopy-theoretic version of a generalization of the notion of topological group, in which the axioms on associativity and inverses are removed.
See Distinguished space and H-space
Hausdorff space
In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space where, for any two distinct points, there exist neighbourhoods of each that are disjoint from each other.
See Distinguished space and Hausdorff space
Infrabarrelled space
In functional analysis, a discipline within mathematics, a locally convex topological vector space (TVS) is said to be infrabarrelled (also spelled infrabarreled) if every bounded barrel is a neighborhood of the origin. Distinguished space and infrabarrelled space are topological vector spaces.
See Distinguished space and Infrabarrelled space
LF-space
In mathematics, an LF-space, also written (LF)-space, is a topological vector space (TVS) X that is a locally convex inductive limit of a countable inductive system (X_n, i_) of Fréchet spaces. Distinguished space and lF-space are topological vector spaces.
See Distinguished space and LF-space
Locally convex topological vector space
In functional analysis and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. Distinguished space and locally convex topological vector space are topological vector spaces.
See Distinguished space and Locally convex topological vector space
Lp space
In mathematics, the spaces are function spaces defined using a natural generalization of the ''p''-norm for finite-dimensional vector spaces.
See Distinguished space and Lp space
Mackey space
In mathematics, particularly in functional analysis, a Mackey space is a locally convex topological vector space X such that the topology of X coincides with the Mackey topology τ(X,X&prime), the finest topology which still preserves the continuous dual. Distinguished space and Mackey space are topological vector spaces.
See Distinguished space and Mackey space
Mathematics
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
See Distinguished space and Mathematics
Metrizable space
In topology and related areas of mathematics, a metrizable space is a topological space that is homeomorphic to a metric space.
See Distinguished space and Metrizable space
Metrizable topological vector space
In functional analysis and related areas of mathematics, a metrizable (resp. pseudometrizable) topological vector space (TVS) is a TVS whose topology is induced by a metric (resp. pseudometric). Distinguished space and metrizable topological vector space are topological vector spaces.
See Distinguished space and Metrizable topological vector space
Montel space
In functional analysis and related areas of mathematics, a Montel space, named after Paul Montel, is any topological vector space (TVS) in which an analog of Montel's theorem holds. Distinguished space and Montel space are topological vector spaces.
See Distinguished space and Montel space
Normed vector space
In mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined.
See Distinguished space and Normed vector space
Polar set
In functional and convex analysis, and related disciplines of mathematics, the polar set A^ is a special convex set associated to any subset A of a vector space X, lying in the dual space X^. Distinguished space and polar set are topological vector spaces.
See Distinguished space and Polar set
Reflexive space
In the area of mathematics known as functional analysis, a reflexive space is a locally convex topological vector space for which the canonical evaluation map from X into its bidual (which is the strong dual of the strong dual of X) is a homeomorphism (or equivalently, a TVS isomorphism).
See Distinguished space and Reflexive space
Semi-reflexive space
In the area of mathematics known as functional analysis, a semi-reflexive space is a locally convex topological vector space (TVS) X such that the canonical evaluation map from X into its bidual (which is the strong dual of X) is bijective.
See Distinguished space and Semi-reflexive space
Separable space
In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence \_^ of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.
See Distinguished space and Separable space
Strong dual space
In functional analysis and related areas of mathematics, the strong dual space of a topological vector space (TVS) X is the continuous dual space X^ of X equipped with the strong (dual) topology or the topology of uniform convergence on bounded subsets of X, where this topology is denoted by b\left(X^, X\right) or \beta\left(X^, X\right).
See Distinguished space and Strong dual space
Topological vector space
In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures investigated in functional analysis. Distinguished space and topological vector space are topological vector spaces.
See Distinguished space and Topological vector space
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.
See Distinguished space and Weak topology