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

Masaru Kada·Kazuo Tomoyasu·Yasuo Yoshinobu
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Abstract

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.

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Masaru Kada, Kazuo Tomoyasu, Yasuo Yoshinobu. 2004-07-21. How many miles to $βω$? -- Approximating $βω$ by metric-dependent compactifications. https://arxiv.org/abs/math/0405311

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