Browder's non-ejective fixed point theorem and a generalization
by Thompson, Stephen, M.S., UNIVERSITY OF MARYLAND, BALTIMORE COUNTY, 2009, 72 pages; 1477375

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 approximation 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.
 
AdviserThomas I. Seidman
SchoolUNIVERSITY OF MARYLAND, BALTIMORE COUNTY
SourceMAI/ 48-06, p. , Jul 2010
Source TypeThesis
SubjectsMathematics
Publication Number1477375
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