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On completeness of quasi-uniform spaces. (English) Zbl 0649.54015

The approach suggested for completions of quasimetric spaces in the paper reviewed below is carried over to a subcategory of quasiuniform spaces containing all uniform spaces: a filter \({\mathcal F}\) in (X,\({\mathcal U})\) is Cauchy if there is a filter \({\mathcal G}\) in X such that for every U in \({\mathcal U}\) there are F in \({\mathcal F}\) and G in \({\mathcal G}\) such that \(F\times G\subset U\). The constructed completion is a reflection in all complete spaces.
Reviewer: M.Hušek

MSC:

54E15 Uniform structures and generalizations
54E52 Baire category, Baire spaces
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