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On right \(K\)-sequentially complete quasi-metric spaces. (English) Zbl 0924.54037
The authors observe that in general right \(K\)-sequential completeness does not imply right \(K\)-completeness, but that implication is true when the space is \(R_1\). They also investigate the relationship between right \(K\)-(sequential) completeness and other well-known notions of quasi-metric completeness. For instance, they prove that every co-stable right \(K\)-sequentially complete quasi-pseudometric space is complete in the sense of Doitchinov and show that a (co-)stable quasi-pseudometric space is compact if and only if it is Cauchy bounded and right \(K\)-sequentially complete. The authors characterize those quasi-metric spaces that admit a quasi-metric right \(K\)-sequential completion. Finally, they show that a metrizable space admits a right \(K\)-sequentially complete quasi-metric if and only if it admits a bicomplete quasi-metric.

MSC:
54E25 Semimetric spaces
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