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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
Posted:
August 20, 2004
MathSciNet review:
2093087
Full-text PDF Free Access
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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
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:
http://dx.doi.org/10.1090/S0002-9939-04-07543-4
PII:
S 0002-9939(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
Posted:
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
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