Rational irreducible plane continua without the fixed-point property

Authors:
Charles L. Hagopian and Roman Manka

Journal:
Proc. Amer. Math. Soc. **133** (2005), 617-625

MSC (2000):
Primary 54F15, 54H25

DOI:
https://doi.org/10.1090/S0002-9939-04-07543-4

Published electronically:
August 20, 2004

MathSciNet review:
2093087

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We define rational irreducible continua in the plane that admit fixed-point-free maps with the condition that all of their tranches have the fixed-point property. This answers in the affirmative a question of Hagopian. The construction is based on a special class of spirals that limit on a double Warsaw circle. The closure of each of these spirals has the fixed-point property.

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Additional Information

**Charles L. Hagopian**

Affiliation:
Department of Mathematics, California State University, Sacramento, Sacramento, California 95819-6051

Email:
hagopian@csus.edu

**Roman Manka**

Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warsaw, Poland

Email:
manka@impan.gov.pl

DOI:
https://doi.org/10.1090/S0002-9939-04-07543-4

Keywords:
Fixed-point property,
rational continua,
irreducible continua of type $\lambda $,
spiral,
double Warsaw circle,
plane continua,
retractions

Received by editor(s):
March 13, 2003

Received by editor(s) in revised form:
October 17, 2003

Published electronically:
August 20, 2004

Additional Notes:
The authors wish to thank Mark Marsh for helpful conversations about the topics of this paper

Communicated by:
Alan Dow

Article copyright:
© Copyright 2004
American Mathematical Society