Uniformizable Cauchy spaces

[摘要] A familyCof filters on a setXis uniformizable if there is a uniformity onXsuch thatCis 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 structureConXwe investigate under what conditions the filteru(C)=⋂F∈CF×Fis a uniformity andCis its collection of Cauchy filters. This problem is treated using Cauchy covering systems.

[学科分类] 数学（综合）