On the G-compactifications of the rational numbers

被引：4

作者：

van Mill, Jan ^{[1
]}

机构：

[1] Vrije Univ Amsterdam, Dept Math, Fac Sci, NL-1081 HV Amsterdam, Netherlands

来源：

MONATSHEFTE FUR MATHEMATIK | 2009年 / 157卷 / 03期

关键词：

G-compactification; Rational numbers; Countable dense homogeneous; SPACE;

D O I：

10.1007/s00605-008-0024-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：257 / 266

页数：10

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