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- Cauchy_space abstract "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.A Cauchy space is a set X and a collection C of proper filters in the power set P(X) such that for each x in X, the ultrafilter at x, U(x), is in C. if F is in C, and F is a subset of G, then G is in C. if F and G are in C and each member of F intersects each member of G, then F ∩ G is in C.An element of C is called a Cauchy filter, and a map f between Cauchy spaces (X,C) and (Y,D) is Cauchy continuous if f(C)⊆D; that is, each the image of each Cauchy filter in X is Cauchy in Y.".
- Cauchy_space wikiPageID "980328".
- Cauchy_space wikiPageLength "2966".
- Cauchy_space wikiPageOutDegree "30".
- Cauchy_space wikiPageRevisionID "617069281".
- Cauchy_space wikiPageWikiLink Cartesian_closed_category.
- Cauchy_space wikiPageWikiLink Category:General_topology.
- Cauchy_space wikiPageWikiLink Cauchy-continuous_function.
- Cauchy_space wikiPageWikiLink Cauchy_net.
- Cauchy_space wikiPageWikiLink Cauchy_sequence.
- Cauchy_space wikiPageWikiLink Complete_metric_space.
- Cauchy_space wikiPageWikiLink Convergence_space.
- Cauchy_space wikiPageWikiLink Directed_set.
- Cauchy_space wikiPageWikiLink English_grammar.
- Cauchy_space wikiPageWikiLink Filter_(mathematics).
- Cauchy_space wikiPageWikiLink General_topology.
- Cauchy_space wikiPageWikiLink Mathematical_analysis.
- Cauchy_space wikiPageWikiLink Metric_space.
- Cauchy_space wikiPageWikiLink Natural_number.
- Cauchy_space wikiPageWikiLink Partially_ordered_group.
- Cauchy_space wikiPageWikiLink Proximity_space.
- Cauchy_space wikiPageWikiLink Singleton_(mathematics).
- Cauchy_space wikiPageWikiLink Subset.
- Cauchy_space wikiPageWikiLink Topological_group.
- Cauchy_space wikiPageWikiLink Topological_space.
- Cauchy_space wikiPageWikiLink Topological_vector_space.
- Cauchy_space wikiPageWikiLink Ultrafilter.
- Cauchy_space wikiPageWikiLink Uniform_space.
- Cauchy_space wikiPageWikiLink Universal_quantification.
- Cauchy_space wikiPageWikiLinkText "Cauchy space".
- Cauchy_space subject Category:General_topology.
- Cauchy_space hypernym Generalization.
- Cauchy_space comment "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.".
- Cauchy_space label "Cauchy space".
- Cauchy_space sameAs Q5054344.
- Cauchy_space sameAs m.03w9x9.
- Cauchy_space sameAs Cauchy_uzayı.
- Cauchy_space sameAs Q5054344.
- Cauchy_space wasDerivedFrom Cauchy_space?oldid=617069281.
- Cauchy_space isPrimaryTopicOf Cauchy_space.