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Fixed points of the bucket handle


Authors: Jan M. Aarts and Robbert J. Fokkink
Journal: Proc. Amer. Math. Soc. 126 (1998), 881-885
MSC (1991): Primary 54H25, 54F15; Secondary 54H11
DOI: https://doi.org/10.1090/S0002-9939-98-04420-7
MathSciNet review: 1459100
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Abstract | References | Similar Articles | Additional Information

Abstract: If a homeomorphism on the bucket handle has an invariant composant, it has a fixed point in that composant. It follows that a homeomorphism on the bucket handle has at least two fixed points. Our methods apply to general Knaster continua.


References [Enhancements On Off] (What's this?)

  • 1. Jan M. Aarts and Robbert J. Fokkink, On composants of the bucket handle, Fund. Math. 139 (1991), no. 3, 193–208. MR 1149412
  • 2. Anatole Beck, Continuous flows in the plane, Springer-Verlag, New York-Heidelberg, 1974. With the assistance of Jonathan Lewin and Mirit Lewin; Die Grundlehren der mathematischen Wissenschaften, Band 201. MR 0500869
  • 3. Howard Cook, W. T. Ingram, and Andrew Lelek, A list of problems known as Houston problem book, Continua (Cincinnati, OH, 1994) Lecture Notes in Pure and Appl. Math., vol. 170, Dekker, New York, 1995, pp. 365–398. MR 1326857
  • 4. D. van Dantzig, Ueber topologisch homogene Kontinua, Fundamenta Mathematicae 14 (1930), 102-125.

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Additional Information

Jan M. Aarts
Affiliation: Technical University Delft, Faculty of Mathematics and Informatics, P.O. Box 5031, 2600 GA Delft, the Netherlands
Email: j.m.aarts@twi.tudelft.nl

Robbert J. Fokkink
Affiliation: Delft Hydraulics, Rotterdamseweg 181, 2600 MH Delft, the Netherlands
Email: fokkink@nsld.wldelft.nl

DOI: https://doi.org/10.1090/S0002-9939-98-04420-7
Keywords: Fixed point, bucket handle, solenoid
Received by editor(s): December 15, 1995
Communicated by: James West
Article copyright: © Copyright 1998 American Mathematical Society