On the G-compactifications of the rational numbers

J. van Mill

doi:10.1007/s00605-008-0024-8

On the G-compactifications of the rational numbers

J. van Mill

Mathematics

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Abstract

We show that for any sufficiently homogeneous metrizable compactum X there is a Polish group G acting continuously on the space of rational numbers Q such that X is its unique G-compactification. This allows us to answer Problem 995 in the 'Open Problems in Topology II' book in the negative: there is a one-dimensional Polish group G acting transitively on Q for which the Hilbert cube is its unique G-completion. © 2008 Springer-Verlag.

Original language	English
Pages (from-to)	257-266
Journal	Monatshefte für Mathematik
Volume	157
DOIs	https://doi.org/10.1007/s00605-008-0024-8
Publication status	Published - 2009

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AB - We show that for any sufficiently homogeneous metrizable compactum X there is a Polish group G acting continuously on the space of rational numbers Q such that X is its unique G-compactification. This allows us to answer Problem 995 in the 'Open Problems in Topology II' book in the negative: there is a one-dimensional Polish group G acting transitively on Q for which the Hilbert cube is its unique G-completion. © 2008 Springer-Verlag.

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JO - Monatshefte für Mathematik

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On the G-compactifications of the rational numbers

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