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International Journal of Mathematics and Mathematical Sciences
Volume 5, Issue 3, Pages 513-527
http://dx.doi.org/10.1155/S0161171282000489

Uniformizable Cauchy spaces

Vrije Universiteit Brussel, Departement Wiskunde, F7, Pleinlaan 2, Brussel 1050 , Belgium

Received 13 April 1981

Copyright © 1982 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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)=FCF×F is a uniformity and C is its collection of Cauchy filters. This problem is treated using Cauchy covering systems.