Continuous Maps of the Interval whose Periodic Points form a Closed Set
- 1 May 1980
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 79 (1) , 127-133
- https://doi.org/10.2307/2042401
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].Keywords
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