## 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:

 5.4e+16 Uniform structures and generalizations 5.4e+53 Baire category, Baire spaces