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...

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

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

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...

Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces. They are generalizations of Banach spaces (normed vector spaces that...

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

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...

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

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...

Kolmogorov in 1935. Suppose X {\displaystyle X} is a topological vector space (TVS) over a topological field K . {\displaystyle \mathbb {K} .} A subset B...

block form. 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...

cases, this topological vector space is not locally convex, and has no continuous non-zero linear forms. Thus the topological dual space contains only...

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...

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...

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

{C}}} is either the category of topological spaces or some subcategory of the category of topological vector spaces (TVSs); If all objects in the category...

(functional analysis) LB-space LF-space – Topological vector space Metrizable topological vector space – A topological vector space whose topology can be defined...

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...

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

Riesz (Riesz 1910). Lp spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces. Because of their key role...

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

and topological structures underlie the linear topological space (in other words, topological vector space) structure. A linear topological space is both...

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

subspaces of this space. Sequence spaces are typically equipped with a norm, or at least the structure of a topological vector space. The most important...

subspace of a topological vector space X , {\displaystyle X,} is a vector subspace M {\displaystyle M} for which there exists some other vector subspace N...

ordered vector space or partially ordered vector space is a vector space equipped with a partial order that is compatible with the vector space operations...

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...

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 linear map from a vector space to its field of scalars (often, the real numbers or the complex numbers). If V is a vector space over a field k, the...