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...

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...

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...

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

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

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...

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

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

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

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

{\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...

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

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...

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

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

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...

{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...

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

Montel space is a barrelled topological vector space in which every closed and bounded subset is compact. A topological vector space (TVS) has the Heine–Borel...

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 and related branches of mathematics, a topological space X is a T0 space or Kolmogorov space (named after Andrey Kolmogorov) if for every pair...

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

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...

In mathematics, the category of topological vector spaces is the category whose objects are topological vector spaces and whose morphisms are continuous...

mathematics, the category of topological spaces, often denoted Top, is the category whose objects are topological spaces and whose morphisms are continuous...

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

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