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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:
 5.4e+26 Semimetric spaces
##### Keywords:
quasi-metric spaces; sequentially complete spaces
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