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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A characterization of maximally almost periodic groups


Author: Ter Jenq Huang
Journal: Proc. Amer. Math. Soc. 75 (1979), 59-62
MSC: Primary 22A05; Secondary 43A60
DOI: https://doi.org/10.1090/S0002-9939-1979-0529213-4
MathSciNet review: 529213
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Abstract: It is proved that a topological group G is maximally almost periodic if and only if G admits an action $ \pi $ on a compact Hausdorff space X such that the transformation group $ (X,G,\pi )$ is equicontinuous and effective. Using this characterization, it is proved that if H is a closed uniform subgroup of a topological group G, then G is maximally almost periodic if and only if H is maximally almost periodic. The latter gives as corollaries the results of Kuranishi, Murakami, Grosser and Moskowitz concerning maximally almost periodic groups.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0529213-4
Keywords: Maximally almost periodic group, equicontinuous transformation group, central topological group
Article copyright: © Copyright 1979 American Mathematical Society