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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$.


References [Enhancements On Off] (What's this?)

  • [1] R. H. Bing, The elusive fixed point property, Amer. Math. Monthly 76 (1969), 119-132. MR 38 #5201. MR 0236908 (38:5201)
  • [2] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)
  • [3] E. Hewitt and K. Stromberg, Real and abstract analysis, a modern treatment of the theory of functions of a real variable, Springer-Verlag, New York and Berlin, 1965. MR 32 #5826. MR 0188387 (32:5826)
  • [4] K. Kuratowski, Topologie. Vol. I, Monografie Mat., Tom 20, PWN, Warsaw, 1948; English transl., PWN, Warsaw; Academic Press, New York, 1966. MR 10, 389; 36 #840. MR 0217751 (36:840)
  • [5] -, Topologie. Vol. II, Monografie Mat., Tom 21, PWN, Warsaw, 1961; English transl., PWN, Warsaw; Academic Press, New York, 1968. MR 24 #A2958; 41 #4467.
  • [6] G. S. Young, Jr., Fixed point theorems for arcwise connected continua, Proc. Amer. Math. Soc. 11 (1960), 880-884. MR 22 #8486. MR 0117711 (22:8486)

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Additional Information

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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