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Complete topological space may refer to: a topological space equipped with an additional Cauchy space structure which is complete, e. g., that it is a complete uniform space with respect to an aforementioned uniformity,
A topological vector space is called a complete topological vector space if any of the following equivalent conditions are satisfied: is a complete uniform space when it is endowed with its canonical uniformity.
In mathematics, a completely metrizable space [1] (metrically topologically complete space [2]) is a topological space (X, T) for which there exists at least one metric d on X such that (X, d) is a complete metric space and d induces the topology T.
A bounded sequentially complete disk in a Hausdorff topological vector space is a Banach disk. [1] A Hausdorff locally convex space that is sequentially complete and bornological is ultrabornological. [2]
A Baire space is a topological space in which every countable intersection of open dense sets is dense in . See the corresponding article for a list of equivalent characterizations, as some are more useful than others depending on the application. (BCT1) Every complete pseudometric space is a Baire space.
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance.More specifically, a topological space is a set whose elements are called points, along with an additional structure called a topology, which can be defined as a set of neighbourhoods for each point that satisfy some axioms ...
A topological vector space where every Cauchy sequence converges is called sequentially complete; in general, it may not be complete (in the sense that all Cauchy filters converge). The vector space operation of addition is uniformly continuous and an open map .
In mathematics, a topological space (X, T) is called completely uniformizable [1] (or Dieudonné complete [2]) if there exists at least one complete uniformity that induces the topology T. Some authors [ 3 ] additionally require X to be Hausdorff .