Fixed points of the bucket handle
HTML articles powered by AMS MathViewer
- by Jan M. Aarts and Robbert J. Fokkink
- Proc. Amer. Math. Soc. 126 (1998), 881-885
- DOI: https://doi.org/10.1090/S0002-9939-98-04420-7
- PDF | Request permission
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
- Jan M. Aarts and Robbert J. Fokkink, On composants of the bucket handle, Fund. Math. 139 (1991), no. 3, 193–208. MR 1149412, DOI 10.4064/fm-139-3-193-208
- Anatole Beck, Continuous flows in the plane, Die Grundlehren der mathematischen Wissenschaften, Band 201, Springer-Verlag, New York-Heidelberg, 1974. With the assistance of Jonathan Lewin and Mirit Lewin. MR 0500869, DOI 10.1007/978-3-642-65548-7
- 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, DOI 10.2307/3618329
- D. van Dantzig, Ueber topologisch homogene Kontinua, Fundamenta Mathematicae 14 (1930), 102–125.
Bibliographic 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
- Received by editor(s): December 15, 1995
- Communicated by: James West
- © Copyright 1998 American Mathematical Society
- 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