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Proceedings of the American Mathematical Society

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

 

 

Continuous maps of the interval whose periodic points form a closed set


Authors: Ethan M. Coven and G. A. Hedlund
Journal: Proc. Amer. Math. Soc. 79 (1980), 127-133
MSC: Primary 54H20; Secondary 58F20
MathSciNet review: 560598
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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].


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DOI: https://doi.org/10.1090/S0002-9939-1980-0560598-7
Article copyright: © Copyright 1980 American Mathematical Society