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Proceedings of the American Mathematical Society

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

 

 

Some results on expansive mappings


Author: Richard K. Williams
Journal: Proc. Amer. Math. Soc. 26 (1970), 655-663
MSC: Primary 54.82
DOI: https://doi.org/10.1090/S0002-9939-1970-0266186-8
MathSciNet review: 0266186
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Abstract: In this paper, expansive mappings are seen as generalizations of expansive homeomorphisms, and known theorems are generalized. The nonexistence of expansive functions on the open unit interval is proven, and a new example of an expansive homeomorphism on the open unit disk is given. Finally, a method for constructing expansive homeomorphisms from expansive mappings is given.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0266186-8
Keywords: Expansive function, expansive mapping, expansive homeomorphism, orbit, iterates, asymptotic points
Article copyright: © Copyright 1970 American Mathematical Society