Between the cofinally complete spaces and the UC spaces

• Autores: Gerald Beer
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 38, Nº 3, 2012, págs. 999-1015
• Idioma: inglés
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• Resumen

  • The local finiteness functional for a metric space (X,d) intuitively describes the radius of the "largest" ball about each point of the space containing at most finitely many points of the space. We give characterizations of those metric spaces in which each sequence along which the functional tends to zero necessarily clusters, placing this class of spaces strictly between the well-studied UC metric spaces and the cofinally complete metric spaces. We produce a subtle formula for the values of the functional for the hyperspace of nonempty closed subsets equipped with Hausdorff distance. Finally, we give necessary and sufficient conditions for the hyperspace to be of this type.