International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 3, Pages 513-527
Uniformizable Cauchy spaces
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 of filters on a set is uniformizable if there is a uniformity on such that 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 on we investigate under what conditions the filter is a uniformity and is its collection of Cauchy filters. This problem is treated using Cauchy covering systems.