On right \(K\)-sequentially complete quasi-metric spaces
type: Item
instance of: scholarly article
title: On right \(K\)-sequentially complete quasi-metric spaces
zbMATH Open document ID: 0924.54037
DOI: 10.1023/A:1006559507624
author: Elena Alemany
author: Salvador Romaguera
published in: Acta Mathematica Hungarica
publication date: 1999-10-31T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 54E25
zbMATH DE Number: 1354877
zbMATH Keywords: quasi-metric spaces
zbMATH Keywords: sequentially complete spaces
MaRDI profile type: Publication
full work available at URL: a:1006559507624
OpenAlex ID: W1810805698
description: scientific article; zbMATH DE number 1354877