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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Recurrence and almost periodicity in a generative transformation group
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by Fred A. Roberson PDF
Proc. Amer. Math. Soc. 32 (1972), 596-598 Request permission

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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Additional Information
  • © Copyright 1972 American Mathematical Society
  • 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