Approximation of fixed point properties of spaces by almost fixed point properties of discrete spaces
by
Rueiher Tsaur
Department of Computing, Imperial College, London SW7 2BZ
Coauthors: Michael B. Smyth

If G and H are graphs, a multifunction f: G --> H is a map that assigns to a vertex x of G a non-empty subset f(x) in H. Let S be a property of sets of vertices of H, then f is said to be a S-multifunction if f sends each vertex of G into a subset of V(H) satisfying S. A graph G is said to possess the S-almost fixed point property (S-afpp) if for any self-mapping S-multifunction f: G --> G there exists a vertex x in V(G) such that {x, y} in E(G) for some y in f(x).

In this paper, we show that almost fixed point properties of discrete spaces and fixed point properties of topological spaces are interdeducible via topological graphs. This leads to a new method to prove various topological fixed point theorems.

Date received: May 15, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagw-47.