On half-completion and bicompletion of quasi-metric spaces. (English) Zbl 0886.54027

Alemany, E.; Romaguera, S.

Commentat. Math. Univ. Carol. 37, No. 4, 749-756 (1996).

Author’s abstract: We characterize the quasi-metric spaces which have a quasi-metric half-completion and deduce that each paracompact co-stable quasi-metric space having a quasi-metric half-completion is metrizable. We also characterize the quasi-metric spaces whose bicompletion is quasi-metric and it is shown that the bicompletion of each quasi-metric compatible with a quasi-metrizable space \(X\) is quasi-metric if and only if \(X\) is finite.

Reviewer: L.Skula (Brno)

MSC:

54E50	Complete metric spaces
54E35	Metric spaces, metrizability
54E15	Uniform structures and generalizations

Keywords:

quasi-metric; quasi-uniform space; half-completion; bicompletion; uniformly weakly regular space