Topological vector space information

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...

convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. They can...

analysis and related areas of mathematics, a complete topological vector space is a topological vector space (TVS) with the property that whenever points get...

put it more abstractly every seminormed vector space is a topological vector space and thus carries a topological structure which is induced by the semi-norm...

be called the algebraic dual space. When defined for a topological vector space, there is a subspace of the dual space, corresponding to continuous linear...

is a compact complete set that is not closed. Any topological vector space is an abelian topological group under addition, so the above conditions apply...

the case of topological vector spaces, which include function spaces, inner product spaces, normed spaces, Hilbert spaces and Banach spaces. In this article...

if it is complete as a topological vector space. If ( X , τ ) {\displaystyle (X,\tau )} is a metrizable topological vector space (such as any norm induced...

general topology Exterior space Hausdorff space – Type of topological space Hilbert space – Type of topological vector space Hemicontinuity Linear subspace –...

pseudometrizable) topological vector space (TVS) is a TVS whose topology is induced by a metric (resp. pseudometric). An LM-space is an inductive limit...

\end{bmatrix}}.} A topological vector space (TVS) X , {\displaystyle X,} such as a Banach space, is said to be a topological direct sum of two vector subspaces...

techniques to bring function spaces as topological vector spaces within reach of the ideas that would apply to normed spaces of finite dimension. Here we...

functional analysis and related areas of mathematics, Schwartz spaces are topological vector spaces (TVS) whose neighborhoods of the origin have a property similar...

mathematics, a metrizable space is a topological space that is homeomorphic to a metric space. That is, a topological space ( X , τ ) {\displaystyle (X...

In mathematics, topological groups are the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time,...

topological vector space is locally convex if and only if its topology is induced by a family of seminorms. Let X {\displaystyle X} be a vector space...

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...

mathematics, nuclear spaces are topological vector spaces that can be viewed as a generalization of finite-dimensional Euclidean spaces and share many of...

also refer to a property of topological vector spaces, or of functions from a topological space into a topological vector space (TVS). A subset B ⊆ X {\displaystyle...

mathematics known as functional analysis, a reflexive space is a locally convex topological vector space for which the canonical evaluation map from X {\displaystyle...

analysis and order theory, an ordered topological vector space, also called an ordered TVS, is a topological vector space (TVS) X that has a partial order...

certain initial topologies, often on topological vector spaces or spaces of linear operators, for instance on a Hilbert space. The term is most commonly used...

a topological homomorphism or simply homomorphism (if no confusion will arise) is the analog of homomorphisms for the category of topological vector spaces...

metrizable topological vector space X {\displaystyle X} (such as a Fréchet space or an F-space) into a Hausdorff topological vector space Y . {\displaystyle...