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Cofinal bicompletenessand quasi-metrizability
Pérez-Peñalver, M.J.
Romaguera, Salvador
1999
Abstract
We introduce the notions of a cofinally bicomplete quasi-uniformity and of a cofinally bicomplete quasi-pseudometric. The Sorgenfrey quasi-metric and the Kofner quasi-metric are interesting examples of cofinally bicomplete quasi-metrics. We observe that the finest quasi-uniformity of any quasi-pseudometrizable bitopological space is cofinally bicomplete and characterize those quasi-pseudometrizable bitopological spaces which admit a cofinally bicomplete quasi-pseudometric. A necessary and sufficient condition for cofinal bicompleteness of quasi-pseudometrizable to-pological spaces is derived. Finally, quasi-metrizable bitopological spaces whose supremum topology is locally compact are characterized.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
30 (1999) suppl.
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
M.J. Pérez-Peñalver and S. Romaguera, "Cofinal bicompletenessand quasi-metrizability", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 30 (1999) suppl., pp. 165-172.
Languages
en
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