Browder's Non-Ejective Fixed Point Theorem and a Generalization
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Title
Browder's Non-Ejective Fixed Point Theorem and a Generalization
Author
Thompson , Stephen
Advisors
Seidman , Thomas I
Program
Mathematics, Applied
UMBC Department
Mathematics and Statistics
Document Type
thesis
Sponsors
University of Maryland , Baltimore County (UMBC)
Keywords
Ejective ; Fixed Point ; Hilbert Cube ; Z-Set
Date Issued
2009-01-01
Abstract
We prove and then generalize Felix Browder's non-ejective fixed point theorem . This is done in several steps . First , following Browder , a rather intricate approxima- tion argument is used to prove that every continuous function from the Hilbert cube into itself has a non-repulsive fixed point . This requires a some background material from topology , which is discussed in the Appendix ; we also prove the Lefschetz fixed point theorem , the homogeneity of the Hilbert cube , and the Alexandroff mapping theorem as intermediate steps in proving the existence of non-repulsive fixed points . Next , again following Browder , we prove the existence of a non-ejective fixed point for every self map of the Hilbert cube . Finally , it is shown that Browder's theorem is true when fixed points are replaced by invariant Z-sets with trivial shape . This is a new generalization of Browder's theorem .
Identifier
10176
Format
application:pdf
Language
en
Collection
UMBC Theses and Disserations .
Rights Statement
This item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please see http://aok.lib.umbc.edu/specoll/repro.php or contact Special Collections at speccoll(at)umbc.edu.
Source
Thompson_umbc_0434M_10176.pdf
Access Rights
Access limited to the UMBC community. Item may possibly be obtained via Interlibrary Loan through a local library, pending author/copyright holder's permission.

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