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Proceedings of the American Mathematical Society

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The fixed point property for homeomorphisms of $ 1$-arcwise connected continua


Author: Lee Mohler
Journal: Proc. Amer. Math. Soc. 52 (1975), 451-456
MSC: Primary 54H25; Secondary 54F50
DOI: https://doi.org/10.1090/S0002-9939-1975-0391064-8
MathSciNet review: 0391064
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Abstract: It is shown that continua which are arcwise connected and contain no simple closed curves have the fixed point property for homeomorphisms, answering in the affirmative a question of Bing. The proof uses measure theoretic techniques. Given a homeomorphism $ h$ of a compact metric space $ X$ onto itself, a probability measure is constructed on $ X$ which is invariant under $ h$.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0391064-8
Keywords: Fixed point property, $ 1$-arcwise connected, Borel set, analytic set, invariant measure
Article copyright: © Copyright 1975 American Mathematical Society

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