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A short short proof of the Cartwright-Littlewood theorem

Author: Morton Brown
Journal: Proc. Amer. Math. Soc. 65 (1977), 372
MSC: Primary 55C20
MathSciNet review: 0461491
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Abstract: Each orientation preserving homeomorphism of the plane that is invariant on a nonseparating bounded continuum has a fixed point on the continuum.

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

  • [1] M. L. Cartwright and J. C. Littlewood, Some fixed point theorems, Ann. of Math. 54 (1951), 1-37. MR 0042690 (13:148f)
  • [2] O. H. Hamilton, A short proof of the Cartwright Littlewood fixed point theorem, Canad. J. Math. 6 (1954), 522-523. MR 0064394 (16:276a)
  • [3] L. E. J. Brouwer, Beweis des Ebenen Translationssatzes, Math. Ann. 72 (1912), 36-54. MR 1511684
  • [4] Harold Bell, A fixed point theorem for planar homeomorphisms, Bull. Amer. Math. Soc. 82 (1976), 778-780. MR 0410710 (53:14457)

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Keywords: Fixed point, homeomorphism, Cartwright-Littlewood
Article copyright: © Copyright 1977 American Mathematical Society

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