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

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...

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

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

LF-space – Topological vector space Metrizable topological vector space – A topological vector space whose topology can be defined by a metric Nuclear space –...

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

analysis, a Banach space (/ˈbɑː.nʌx/, Polish pronunciation: [ˈba.nax]) is a complete normed vector space. Thus, a Banach space is a vector space with a metric...

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...

subset Bounded set (topological vector space) – Generalization of boundedness Locally convex topological vector space – Vector space with a topology defined...

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...

complete. Cauchy net Complete space Complete topological vector space Quasi-complete space Topological vector space Uniform space Narici & Beckenstein...

In mathematics, a completely metrizable space (metrically topologically complete space) is a topological space (X, T) for which there exists at least one...

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

continuous function. Every topological group G {\displaystyle G} (in particular, every topological vector space) becomes a uniform space if we define a subset...

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

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

{\displaystyle \{0\}} is a compact complete set that is not closed. Any topological vector space is an abelian topological group under addition, so the above...

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

authors use the term topologically complete for a wider class of topological spaces, the completely uniformizable spaces. A topological space homeomorphic to...

fallback Complete topological vector space – A TVS where points that get progressively closer to each other will always converge to a point Uniform space – Topological...

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...

different ways to construct a topological tensor product of two topological vector spaces. For Hilbert spaces or nuclear spaces there is a simple well-behaved...

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...

claimed to be homeomorphic to the topological quotient. Goreham, Anthony. Sequential convergence in Topological Spaces Archived 2011-06-04 at the Wayback...

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

fallback Ordered topological vector space Ostrowski's theorem – On all absolute values of rational numbers Topological abelian group – topological group whose...

multiplication, it is a real vector space. The coordinates over any basis of the elements of a real vector space form a real coordinate space of the same dimension...

measure theory in topological vector spaces refers to the extension of measure theory to topological vector spaces. Such spaces are often infinite-dimensional...

such as topological groups, topological rings, topological fields and topological vector spaces over the latter. Local fields are topological fields important...

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