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Proceedings of the American Mathematical Society

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

 

 

On pointwise periodic transformation groups


Author: S. K. Kaul
Journal: Proc. Amer. Math. Soc. 27 (1971), 391-394
MSC: Primary 54.80
DOI: https://doi.org/10.1090/S0002-9939-1971-0267551-6
MathSciNet review: 0267551
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Abstract: Let $ X$ be a connected and metrizable manifold without boundary, and $ (X,T)$ a transformation group. We prove that if $ T$ is countable and pointwise periodic then $ T$ is periodic. This is a generalization of a result of Montgomery, which says that if $ h$ is a pointwise periodic homeomorphism of $ X$ onto itself then $ h$ is periodic.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0267551-6
Keywords: Transformation group, manifold, pointwise periodic, periodic, equicontinuous, lower semicontinuous
Article copyright: © Copyright 1971 American Mathematical Society