Total boundedness in metrizable spaces

• Autores: Gerald Beer, Camillo Costantini, Sandro Levi
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 37, Nº 4, 2011, págs. 1347-1362
• Idioma: inglés
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• Resumen

  • We show that a metric space (X,d ) is separable if and only if the bornology of its d-bounded subsets agrees with the bornology of ?-totally bounded subsets with respect to some equivalent remetrization ?. We also show that the bornology of d-totally bounded subsets agrees with the bornology of ?-bounded subsets with respect to some equivalent remetrization if and only if the former bornology has a countable cofinal subfamily. Finally, we characterize those bornologies on a metrizable space that are bornologies of totally bounded sets as determined by some metric compatible with the topology