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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
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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Keywords: Maximally almost periodic group, equicontinuous transformation group, central topological group
Article copyright: © Copyright 1979 American Mathematical Society

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