DSpace Collection:
http://hdl.handle.net/10077/4314
Sun, 05 Feb 2023 13:30:39 GMT2023-02-05T13:30:39Z$\mu-embedded$ sets in topological spaces
http://hdl.handle.net/10077/4349
Title: $\mu-embedded$ sets in topological spaces
Authors: Tarres, Juan; Sanz, M. Agripina
Abstract: We define the concept of a $\mu-embedded$ set in a completely regular topological space X and we state that every v-embedded set in X is $\mu-embedded$ in X. Also, we give an example
which proves that the converse is not true.Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10077/43491999-01-01T00:00:00ZA note on quasi-k-spaces
http://hdl.handle.net/10077/4348
Title: A note on quasi-k-spaces
Authors: Sanchis, Manuel
Abstract: We prove that for a regular Hausdorff space X the following conditions are equivalent: (1) X is locally compact, (2) for each quasi-k-space Y, the product space $X \times Y$ is also a quasi-k-space.Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10077/43481999-01-01T00:00:00ZCofinal bicompletenessand quasi-metrizability
http://hdl.handle.net/10077/4347
Title: Cofinal bicompletenessand quasi-metrizability
Authors: Pérez-Peñalver, M.J.; Romaguera, Salvador
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.Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10077/43471999-01-01T00:00:00ZA non quasi-metric completion for quasi-metric spaces
http://hdl.handle.net/10077/4346
Title: A non quasi-metric completion for quasi-metric spaces
Authors: Lowen, R.; Vaughan, D.
Abstract: The authors have previously presented a completion theory for those approach spaces which have an underlying To topology – these include all quasi-metric spaces. This theory extends the existing completion theory for uniform approach spaces, which in turn generalizes that for metric spaces. This new completion theory, moreover, has an interesting relationship with the completion theory for nearness spaces. The theory allows every quasi-metric space to be completed, and remarkably such completions need not again be quasimetric; this situation contrasts with all other previously introduced completion theories for quasi-metric spaces (e.g. [12, 3, 9]). In this paper we present an example of a non-quasi-metric completion, and we give some conditions which ensure that the completion is again quasi-metric. This investigation leads us to favour one particular form of Cauchy sequence in quasi-metric spaces.Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10077/43461999-01-01T00:00:00Z