of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize...

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...

typically not Banach spaces. A Fréchet space X {\displaystyle X} is defined to be a locally convex metrizable topological vector space (TVS) that is complete...

points. More generally, each compact convex set in a locally convex topological vector space is the closed convex hull of its extreme points (the Krein–Milman...

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

Characterization of normable spaces Locally convex topological vector space – a vector space with a topology defined by convex open sets Space (mathematics) – mathematical...

DF-space – class of special local-convex spacePages displaying wikidata descriptions as a fallback Fréchet space – Locally convex topological vector space...

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

generally, every locally convex topological vector space is locally connected, since each point has a local base of convex (and hence connected) neighborhoods...

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

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...

zero vector. A barrelled set or a barrel in a topological vector space is a set that is convex, balanced, absorbing, and closed. Barrelled spaces are studied...

A nuclear space is a locally convex topological vector space A {\displaystyle A} such that for every locally convex topological vector space B {\displaystyle...

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

usual vector space topology of R n , {\displaystyle \mathbb {R} ^{n},} hence ℓ n p {\displaystyle \ell _{n}^{p}} is a locally convex topological vector space...

Distortion problem Interpolation space Locally convex topological vector space – Vector space with a topology defined by convex open sets Modulus and characteristic...

compact convex sets in locally convex topological vector spaces (TVSs). Krein–Milman theorem—A compact convex subset of a Hausdorff locally convex topological...

(topological vector space) – Generalization of boundedness Locally convex topological vector space – Vector space with a topology defined by convex open...

a continuous linear transformation between topological vector spaces. An operator between two normed spaces is a bounded linear operator if and only if...

(sD)=(\min _{}\{|r|,|s|\})D.} The absolutely convex hull of a bounded set in a locally convex topological vector space is again bounded. If D {\displaystyle...

Connectedness is one of the principal topological properties that distinguish topological spaces. A subset of a topological space X {\displaystyle X} is a connected...

is Fréchet, meaning that it is a complete, metrizable, locally convex topological vector space (TVS). However, this topology is rather pathological: there...

theorem to locally convex topological vector spaces, which may be of infinite dimension. It asserts that if K {\displaystyle K} is a nonempty convex closed...

that applies to all normed spaces Locally convex topological vector space – Vector space with a topology defined by convex open sets Operator theory –...

Fréchet space: a locally convex topological vector space whose topology can be induced by a complete translation-invariant metric. The space Qp of p-adic...

topological vector spaces; it dates to a 1935 paper of John von Neumann. This definition has the appealing property that, in a locally convex space endowed...

functional analysis, a discipline within mathematics, a locally convex topological vector space (TVS) is said to be infrabarrelled (also spelled infrabarreled)...

continuous dual space. If we give X the weak topology 𝜎(X, Y) then X𝜎(X, Y) is a Hausdorff locally convex topological vector space (TVS) and 𝜎(X, Y)...

F-space Fréchet space Krein–Milman theorem Locally convex topological vector space Mackey topology Mackey–Arens theorem Montel space Polar set Polar topology...

generally in a locally convex topological vector space) is the convex hull of its extreme points. However, this may not be true for convex sets that are...