How many miles to $βω$? -- Approximating $βω$ by metric-dependent compactifications

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It is known that the Stone-Čech compactification of a non-compact metrizable space $X$ is approximated by the collection of Smirnov compactifications of $X$ for all compatible metrics on $X$. We investigate the smallest cardinality of a set $D$ of compatible metrics on the countable discrete space $ω$ such that, the Stone-Čech compactification of $ω$ is approximated by Smirnov compactifications for all metrics in $D$, but any finite subset of $D$ does not suffice. We also study the corresponding cardinality for Higson compactifications.
v3: Unified old sections 1 and 2 into new section 1, and deleted some basic lemmata to shorten the article

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General Topology, Logic, 03E17; 03E35; 54D35; 54H05

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http://salesiana.dossiersoluciones.com/handle/123456789/71213

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0405311
 http://arxiv.org/abs/math/0405311

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arXiv