Uniformizable Cauchy spaces
Open Access
- 1 January 1982
- journal article
- research article
- Published by Wiley in International Journal of Mathematics and Mathematical Sciences
- Vol. 5 (3) , 513-527
- https://doi.org/10.1155/s0161171282000489
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.Keywords
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