Fixed points of orientation reversing homeomorphisms of the plane

Author:
Krystyna Kuperberg

Journal:
Proc. Amer. Math. Soc. **112** (1991), 223-229

MSC:
Primary 54F15

DOI:
https://doi.org/10.1090/S0002-9939-1991-1064906-X

MathSciNet review:
1064906

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be an orientation reversing homeomorphism of the plane onto itself. If is a plane continuum invariant under , then has a fixed point in . Furthermore, if at least one of the bounded complementary domains of is invariant under , then has at least two fixed points in .

**[1]**Harold Bell,*A fixed point theorem for planar homeomorphisms*, Bull. Amer. Math. Soc.**82**(1976), 778-780. MR**0410710 (53:14457)****[2]**-,*A fixed point theorem for plane homeomorphisms*, Fund. Math.**100**(1978), 119-128. MR**0500879 (58:18386)****[3]**-, preliminary manuscript.**[4]**Beverly Brechner,*Prime ends, indecomposable continua, and the fixed point property*, Topology Proc.**4**(1979), 227-234. MR**583705 (81j:54053)****[5]**Morton Brown,*A short short proof of the Cartwright-Littlewood fixed point theorem*, Proc. Amer. Math. Soc.**65**(1977), 372. MR**0461491 (57:1476)****[6]**M. L. Cartwright and J. C. Littlewood,*Some fixed point theorems*, Ann. of Math.**54**(1951), 1-37. MR**0042690 (13:148f)****[7]**O. H. Hamilton,*A short proof of the Cartwright-Littlewood fixed point theorem*, Canad. J. Math.**6**(1954), 522-524. MR**0064394 (16:276a)****[8]**Sze-Tsen Hu,*Homotopy theory*, Academic Press, 1959. MR**0106454 (21:5186)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1064906-X

Keywords:
Fixed point

Article copyright:
© Copyright 1991
American Mathematical Society