Rational irreducible plane continua without the fixed-point property
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- by Charles L. Hagopian and Roman Mańka PDF
- Proc. Amer. Math. Soc. 133 (2005), 617-625 Request permission
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.References
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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 Mańka
- Affiliation: Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warsaw, Poland
- Email: manka@impan.gov.pl
- 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
- © Copyright 2004 American Mathematical Society
- 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
- MathSciNet review: 2093087