期刊
TOPOLOGY AND ITS APPLICATIONS
卷 111, 期 1-2, 页码 195-205出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/S0166-8641(99)00185-6
关键词
topological group; uniformity; semigroup; relation; compactification
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.
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