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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A characterization of the equicontinuous structure relation


Authors: Robert Ellis and Harvey Keynes
Journal: Trans. Amer. Math. Soc. 161 (1971), 171-183
MSC: Primary 54.82
MathSciNet review: 0282357
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Abstract: The main result in the paper is to show that in a large class of minimal transformation groups (including those with abelian phase groups, and point-distal transformation groups), the equicontinuous structure relation is precisely the regionally proximal relation. The techniques involved enable one to recover and extend the previously known characterizations. Several corollaries are indicated, among which the most important is a new criterion (which is easily applicable) for the existence of a nontrivial equicontinuous image of a given transformation group.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0282357-4
Keywords: Equicontinuous structure relation, minimal transformation groups, distal and point-distal transformation groups, abelian transformation groups, locally almost periodic transformation groups, distal extensions
Article copyright: © Copyright 1971 American Mathematical Society