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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.
- [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
(13,148f)
- [2]
O.
H. Hamilton, A short proof of the Cartwright-Littlewood fixed point
theorem, Canadian J. Math. 6 (1954), 522–524.
MR
0064394 (16,276a)
- [3]
L.
E. J. Brouwer, Beweis des ebenen Translationssatzes, Math.
Ann. 72 (1912), no. 1, 37–54 (German). MR
1511684, http://dx.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
(53 #14457), http://dx.doi.org/10.1090/S0002-9904-1976-14161-4
- [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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DOI:
http://dx.doi.org/10.1090/S0002-9939-1977-0461491-0
PII:
S 0002-9939(1977)0461491-0
Keywords:
Fixed point,
homeomorphism,
Cartwright-Littlewood
Article copyright:
© Copyright 1977 American Mathematical Society
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