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

Doichinov, D.

C. R. Acad. Bulg. Sci. 41, No. 7, 5-8 (1988).

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

Keywords:

completeness; quasiuniform spaces; completion; reflection; complete spaces