## On countably compact quasi-pseudometrizable spaces.(English)Zbl 0706.54027

Summary: We prove the following results: (1) A quasi-metrizable space is compact if and only if every compatible quasi-metric has a quasi-metric left d- sequential completion. (2) A quasi-pseudometrizable space is countably compact if and only if every compatible quasi-pseudometric is pointwise bounded. (3) A quasi-pseudometrizable space is compact if and only if every compatible quasi-pseudometric is precompact.

### MSC:

 54E45 Compact (locally compact) metric spaces 54E52 Baire category, Baire spaces 54D30 Compactness 54E35 Metric spaces, metrizability 54E50 Complete metric spaces