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

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

2004-05-16

arxiv.org/abs/math/0405311v3

Mathematics

General Topology

v3: Unified old sections 1 and 2 into new section 1, and deleted some basic lemmata to shorten the article

Scientific paper

It is known that the Stone-\v{C}ech 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 $\omega$ such that, the Stone-\v{C}ech compactification of $\omega$ 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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