A short short proof of the Cartwright-Littlewood theorem
Author:
Morton Brown
Journal:
Proc. Amer. Math. Soc. 65 (1977), 372
MSC:
Primary 55C20
DOI:
https://doi.org/10.1090/S0002-9939-1977-0461491-0
MathSciNet review:
0461491
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Abstract | References | Similar Articles | Additional Information
Abstract: Each orientation preserving homeomorphism of the plane that is invariant on a nonseparating bounded continuum has a fixed point on the continuum.
- [1] M. L. Cartwright and J. E. Littlewood, Some fixed point theorems, Ann. of Math. (2) 54 (1951), 1–37. With appendix by H. D. Ursell. MR 0042690, https://doi.org/10.2307/1969308
- [2] O. H. Hamilton, A short proof of the Cartwright-Littlewood fixed point theorem, Canadian J. Math. 6 (1954), 522–524. MR 0064394
- [3] L. E. J. Brouwer, Beweis des ebenen Translationssatzes, Math. Ann. 72 (1912), no. 1, 37–54 (German). MR 1511684, https://doi.org/10.1007/BF01456888
- [4] Harold Bell, A fixed point theorem for plane homeomorphisms, Bull. Amer. Math. Soc. 82 (1976), no. 5, 778–780. MR 0410710, https://doi.org/10.1090/S0002-9904-1976-14161-4
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1977-0461491-0
Keywords:
Fixed point,
homeomorphism,
Cartwright-Littlewood
Article copyright:
© Copyright 1977
American Mathematical Society