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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
Published electronically: August 20, 2004
MathSciNet review: 2093087
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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

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

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