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| Title: | Homeomorphisms of knaster continua |
| Authors: | Ssembatya, Vincent A. |
| Keywords: | Knaster continua
Homeomorphisms
Knaster continuum
Bowen's theorem
Buckethandle
Unit intervals
Mathematical theories
Solenoids
Higher dimensional continua
Topological groups |
| Issue Date: | 2001 |
| Publisher: | University of Florida |
| Abstract: | In this thesis we investigate homeomorphisms of Knaster continua. We determine the minimum number of fixed-points homeomorphisms of these continua must have. This analysis is related to a question raised by William S. Mahavier on whether a homeomorphism on the Knaster bucket handle must have at least two fixed points. It is proved that an isotopy between homeomorphisms of the Knaster continuum can be lifted to an isotopy between homeomorphisms of the solenoid. We give necessary and sufficient conditions for a homeomorphism of the Knaster continuum to have at least two fixed points. We construct a Knaster continuum on which every homeomorphism has either uncountably many fixed points or uncountably many points of period 2. We determine the minimum number of fixed points a homeomorphism on the Knaster continuum can have. We construct an example to show that Bowen's theorem on entropy of quotients on compact spaces does not readily generalize to non-compact spaces.
We generalize the definitions of Knaster continua to constructions via toral homomorphisms. We show that homeomorphism on these continua (in the odd dimension case) lift to homeomorphisms to the solenoid and end with some questions for further research. |
| Description: | A dissertation presented to the Graduate School of the University of Florida in partial fulfillment of the requirements for the degree of Doctor of Philosophy |
| URI: | http://hdl.handle.net/123456789/1361 |
| Appears in Collections: | Theses & Dissertations (Science)
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