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Proceedings of the American Mathematical Society

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

 

 

Sets of recurrent points of continuous maps of the interval


Author: Jin Cheng Xiong
Journal: Proc. Amer. Math. Soc. 95 (1985), 491-494
MSC: Primary 58F20; Secondary 54H20
MathSciNet review: 806094
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Abstract: For a continuous map of the interval the following conditions are equivalent: (1) the period of every periodic point is a power of 2, (2) $ {\overline R ^{( + )}} \cap {\overline R ^{( - )}} - R = \phi $, and (3) $ \overline R - R$ is countable, where $ R$ denotes the set of recurrent points. $ \overline R $ is the closure of $ R$, and $ {\overline R ^{( + )}}$ (or $ {\bar R^{( - )}}$) is the right-side closure (left-side closure, respectively) of $ R$.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0806094-5
Article copyright: © Copyright 1985 American Mathematical Society