Convexity and the Brouwer Fixed Point Theorem
by
Władysław Kulpa
University of Silesia, Katowice, Poland

A notion of convexity for topological spaces is introduced in order to obtain the following generalization of the Brouwer-Schauder Fixed Point Theorem;

Each compact Hausdorff convex and locally convex topological space has the fixed point property

A simple example shows that the assumption of local convexity is necessary. The theorem and the example are related to still unsolved Problem 54 from the Scottish Book; Is essential the assumption of local convexity for linear topological spaces?

Date received: July 28, 1997

Copyright © 1997 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 # caap-09.