On the G-compactifications of the rational numbers

J. van Mill

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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 languageEnglish
Pages (from-to)257-266
JournalMonatshefte für Mathematik
Publication statusPublished - 2009


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