General topology

Cauchy space

In general topology and analysis, a Cauchy space is a generalization of metric spaces and uniform spaces for which the notion of Cauchy convergence still makes sense. Cauchy spaces were introduced by H. H. Keller in 1968, as an axiomatic tool derived from the idea of a Cauchy filter, in order to study completeness in topological spaces. The category of Cauchy spaces and Cauchy continuous maps is Cartesian closed, and contains the category of proximity spaces. (Wikipedia).

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Related pages

Topological space | Metric space | Ultrafilter (set theory) | Cauchy sequence | Topological group | Topological vector space | Mathematical analysis | Directed set | Filter (set theory) | Uniform space | Proximity space | Cauchy-continuous function | General topology | Natural number | Family of sets | Subset | Category (mathematics) | Morphism | Convergence space | Complete metric space | Power set