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Proceedings of the American Mathematical Society

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

 

 

Extending expansive homeomorphisms


Author: J. D. Wine
Journal: Proc. Amer. Math. Soc. 86 (1982), 531-534
MSC: Primary 54H20; Secondary 54C10
DOI: https://doi.org/10.1090/S0002-9939-1982-0671230-8
MathSciNet review: 671230
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Abstract: In previous work on extensions of expansive homeomorphisms there has always been a finiteness condition placed on the remainder. In this note we give a necessary and sufficient condition for a self-homeomorphism to be expansive by restrictions on orbits, and then use this to give a sufficient condition for the homeomorphic extension of an expansive homeomorphism to be expansive. Two examples are given wherein the homeomorphic extensions of expansive homeomorphism are examined relative to the conditions of the theorem.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0671230-8
Keywords: Expansive homeomorphism, extending homeomorphisms, orbits
Article copyright: © Copyright 1982 American Mathematical Society