Uniformizable Cauchy spaces

Eva Lowen-Colebunders

International Journal of Mathematics and Mathematical Sciences, 1982, vol. 5, 1-15

Abstract:

A family C of filters on a set X is uniformizable if there is a uniformity on X such that C is its collection of Cauchy filters. Using the theory of completions and Cauchy continuous maps for Cauchy spaces, we obtain characterizations of uniformizable Cauchy spaces. In particular, given a Cauchy structure C on X we investigate under what conditions the filter u ( C ) = ⋂ F ∈ C F × F is a uniformity and C is its collection of Cauchy filters. This problem is treated using Cauchy covering systems.

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:404620

DOI: 10.1155/S0161171282000489

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