Supercompleteness and related properties of k-metric spaces are investigated (a k-metric space is a uniform space which admits a base of uniform coverings which is well ordered by star-refinement by an uncountable regular cardinal k). It is shown in ZFC that supercompleteness is not equivalent to completeness for k-metric spaces. On the other hand, a k-metric space is k-compact iff it is supercomplete and k-totally bounded. The space 2^k with the k-product uniformity is supercomplete iff k is weakly compact. There is a complete k-totally bounded k-metric space which is not k-compact iff there is a k-Aronszajn tree.

On Supercomplete omega_mu-Metric Spaces

ARTICO, GIULIANO;MARCONI, UMBERTO;
1996

Abstract

Supercompleteness and related properties of k-metric spaces are investigated (a k-metric space is a uniform space which admits a base of uniform coverings which is well ordered by star-refinement by an uncountable regular cardinal k). It is shown in ZFC that supercompleteness is not equivalent to completeness for k-metric spaces. On the other hand, a k-metric space is k-compact iff it is supercomplete and k-totally bounded. The space 2^k with the k-product uniformity is supercomplete iff k is weakly compact. There is a complete k-totally bounded k-metric space which is not k-compact iff there is a k-Aronszajn tree.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/2464020
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