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Rational irreducible plane continua without the fixed-point property |
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| Authors: | Charles L. Hagopian Roman Manka |
| Affiliation: | Department of Mathematics, California State University, Sacramento, Sacramento, California 95819-6051 ; Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, 00-956 Warsaw, Poland |
| 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. |
| Keywords: | Fixed-point property rational continua irreducible continua of type $lambda $ spiral double Warsaw circle plane continua retractions |
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