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

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