http://www.openstarts.units.it:80/dspace/handle/10077/4314 2013-05-20T22:25:16Z http://www.openstarts.units.it:80/dspace/handle/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. Type: Articolo 1999-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/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. Type: Articolo 1999-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/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. Type: Articolo 1999-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/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. Type: Articolo 1999-01-01T00:00:00Z