International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 3, Pages 513-527
doi:10.1155/S0161171282000489

Uniformizable Cauchy spaces

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∈CF×F is a uniformity and C is its collection of Cauchy filters. This problem is treated using Cauchy covering systems.