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On countably compact quasi-pseudometrizable spaces
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AbstractWe 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 quasipseudometrizable 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.
Cambridge University Press (CUP)
Title: On countably compact quasi-pseudometrizable spaces
Description:
AbstractWe 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 quasipseudometrizable 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.
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