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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Continuous maps of the interval with finite nonwandering set


Author: Louis Block
Journal: Trans. Amer. Math. Soc. 240 (1978), 221-230
MSC: Primary 54H20; Secondary 58F20
DOI: https://doi.org/10.1090/S0002-9947-1978-0474240-2
MathSciNet review: 0474240
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Abstract: Let f be a continuous map of a closed interval into itself, and let $ \Omega (f)$ denote the nonwandering set of f. It is shown that if $ \Omega (f)$ is finite, then $ \Omega (f)$ is the set of periodic points of f. Also, an example is given of a continuous map g, of a compact, connected, metrizable, one-dimensional space, for which $ \Omega (g)$ consists of exactly two points, one of which is not periodic.


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DOI: https://doi.org/10.1090/S0002-9947-1978-0474240-2
Article copyright: © Copyright 1978 American Mathematical Society