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Proceedings of the American Mathematical Society

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



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
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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Keywords: Fixed point property, <IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$1$">-arcwise connected, Borel set, analytic set, invariant measure
Article copyright: © Copyright 1975 American Mathematical Society