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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- © Copyright 1975 American Mathematical Society
- 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