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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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Continuous maps of the interval whose periodic points form a closed set
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by Ethan M. Coven and G. A. Hedlund PDF
Proc. Amer. Math. Soc. 79 (1980), 127-133 Request permission

Abstract:

We show that for a continuous map of a closed interval to itself, if the set of periodic points is closed, then every recurrent point is periodic. If, furthermore, the set of least periods of the periodic points is finite, then every nonwandering point is periodic. This answers a question of L. Block [Proc. Amer. Math. Soc. 67 (1977), 357-360].
References
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 79 (1980), 127-133
  • MSC: Primary 54H20; Secondary 58F20
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0560598-7
  • MathSciNet review: 560598