How many miles to beta-X? -- d miles, or just one foot

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It is known that the Stone-Cech compactification of a metrizable space X is approximated by the collection of Smirnov compactifications of X for all compatible metrics on X. If we confine ourselves to locally compact separable metrizable spaces, the corresponding statement holds for Higson compactifications. We investigate the smallest cardinality of a set D of compatible metrics on X such that the Stone-Cech compactification of X is approximated by Smirnov or Higson compactifications for all metrics in D. We prove that it is either the dominating number or 1 for a locally compact separable metrizable space.
V2: minor linguistic corrections

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General Topology, 54D35; 03E17

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http://salesiana.dossiersoluciones.com/handle/123456789/101001

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0412547
 http://arxiv.org/abs/math/0412547

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arXiv