International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 3, Pages 513-527

Uniformizable Cauchy spaces

Eva Lowen-Colebunders

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

Received 13 April 1981

Copyright © 1982 Eva Lowen-Colebunders. 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.


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.