A topological transformation group without non-trivial equivariant compactifications

被引：3
|
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
收藏
页码：1 / 17
页数：17
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