On distal and equicontinuous compact right topological groups
type: Item
instance of: scholarly article
title: On distal and equicontinuous compact right topological groups
zbMATH Open document ID: 0828.22001
DOI: 10.1155/S0161171294000529
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1996-01-02T00:00:00Z
full work available at URL: https://eudml.org/doc/47313
full work available at URL: issue-2.html
review text: R. Ellis showed that a flow on a compact space is distal if and only if its enveloping semigroup is a group. However, rather surprisingly, if \(G\) is a compact left-topological group then the flow on \(G\) consisting of left translations need be neither distal nor equicontinuous. It is shown that the flow on \(G\) is distal resp. equicontinuous if and only if every continuous function on \(G\) is distal resp. almost periodic. The paper then goes on to try to determine the set of continuous almost periodic functions on \(G\). Solutions are found when \(G\) has dense topological centre, but the situation is shown to be complicated in general.
reviewed by: John W.Baker
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 569407
zbMATH Keywords: distal flow
zbMATH Keywords: equicontinuous flow
zbMATH Keywords: continuous almost periodic functions
zbMATH Keywords: enveloping semigroup
zbMATH Keywords: compact left-topological group
author: Paul Milnes
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 569407