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On the G-compactifications of the rational numbers |
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| Authors: | Jan van Mill |
| Institution: | (1) School of Mathematics and Statistics, The University of Sydney, Sydney, NSW, 2006, Australia;(2) Present address: Mathematisches Seminar der Universit?t Hamburg, Bundesstr. 55, 20146 Hamburg, Germany;(3) Science Institute, University of Iceland, Dunhaga 3, 107 Reykjav?k, Iceland |
| 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 \mathbbQ{\mathbb{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 \mathbbQ{\mathbb{Q}} for which the Hilbert cube is its unique G-completion. |
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