A topological transformation group without non-trivial equivariant compactifications

被引：5

作者：

Pestov, Vladimir G. ^{[1
,2
]}

机构：

[1] Univ Ottawa, Dept Math & Stat, 585 King Edward Ave, Ottawa, ON K1N 6N5, Canada

[2] Univ Fed Santa Catarina, Dept Matemat, BR-8800900 Florianopolis, SC, Brazil

来源：

ADVANCES IN MATHEMATICS | 2017年 / 311卷

关键词：

Topological transformation group; Equivariant compactification; SPACE; UNIVERSAL; URYSOHN;

D O I：

10.1016/j.aim.2017.02.023

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

There is a countable metrizable group acting continuously on the space of rationals in such a way that the only equivariant compactification of the space is a singleton. This is obtained by a recursive application of a construction due to Megrelishvili, which is a metric fan equipped with a certain group of homeomorphisms. The question of existence of a topological transformation group with the property in the title was asked by Yu.M. Smirnov in the 1980s. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：1 / 17

页数：17

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