The Roelcke compactification of groups of homeomorphisms

被引：10

作者：

Uspenskij, VV ^{[1
]}

机构：

[1] Ohio Univ, Dept Math, Athens, OH 45701 USA

来源：

TOPOLOGY AND ITS APPLICATIONS | 2001年 / 111卷 / 1-2期

关键词：

topological group; uniformity; semigroup; relation; compactification;

D O I：

10.1016/S0166-8641(99)00185-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X be a zero-dimensional compact space such that all cion-empty clopen subsets of X are homeomorphic to each other, and let Aut X be the group of all self-homeomorphisms of X, equipped with the compact-open topology. We prove that the Roelcke compactification of AutX can be identified with the semigroup of all closed relations on X whose domain and range are equal to X. We use this to prove that the group Aut X is topologically simple and minimal. (C) 2001 Elsevier Science B.V. All rights reserved.

引用

页码：195 / 205

页数：11