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Proceedings of the American Mathematical Society

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

 

 

Recurrence and almost periodicity in a generative transformation group


Author: Fred A. Roberson
Journal: Proc. Amer. Math. Soc. 32 (1972), 596-598
MSC: Primary 54H15
DOI: https://doi.org/10.1090/S0002-9939-1972-0293609-2
MathSciNet review: 0293609
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Abstract: A point p in a transformation group (X, T, II) is recurrent if for every neighborhood U of p there is an extensive set $ E \subset T$ such that $ pE \subset U$. The point p is almost periodic if there is a syndetic set $ A \subset T$ such that $ pA \subset U$. This paper proves that a recurrent point in a locally compact, generative transformation group with an equicontinuous neighborhood must also be almost periodic.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0293609-2
Keywords: Transformation group, generative, recurrent, almost periodic, equicontinuous
Article copyright: © Copyright 1972 American Mathematical Society