Dense orbits of automorphisms and compactness of groups
type: Item
instance of: scholarly article
title: Dense orbits of automorphisms and compactness of groups
zbMATH Open document ID: 0568.28013
DOI: 10.1016/0166-8641(85)90030-6
author: Nobuo Aoki
published in: Topology and its Applications
publication date: 1985-01-01T00:00:00Z
review text: This paper deals with the Halmos' question of whether locally compact groups which admit ergodic (under the Haar measure) automorphisms are compact. The question was solved in [\textit{M. Rajagopalan}, Proc. Am. Math. Soc. 17, 372-376 (1966; Zbl 0166.027), \textit{R. Kaufman} and \textit{M. Rajagapalan}, Mich. Math. J. 13, 373-374 (1966; Zbl 0156.262), \textit{T. S. Wu}, Math. Z. 96, 256-258 (1967; Zbl 0163.027), \textit{S. A. Yuzoinsij}, Russian Math. Surveys 22, 47-52 (1967)] with exception of the totally disconnected case, however had remained open for the exceptional case. The autor gives, by using the technique in dynamical systems, an answer for this case.
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 28D15
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 54G05
Mathematics Subject Classification ID: 54E45
Mathematics Subject Classification ID: 22B05
zbMATH DE Number: 3906798
zbMATH Keywords: Halmos' question of whether locally compact groups which admit ergodic under the Haar measure automorphisms are compact
zbMATH Keywords: totally disconnected case
MaRDI profile type: Publication
full work available at URL: 0166-8641(85)90030-6
OpenAlex ID: W1977232116
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description: scientific article; zbMATH DE number 3906798