Fixed point and min − max theorems

D. G. Bourgin

Vol. 45 (1973), No. 2, 403–412

DOI: 10.2140/pjm.1973.45.403

Abstract

The unifying idea in this paper is the existence and uniqueness of cohomology homomorphisms in an admissible range of dimensions, induced by suitable restricted upper semicontinuous homotopies. One consequence of this underlying homotopy result is a fixed point theorem for multiple valued self maps of an n-ball which allows nonacyclic images of points. Another consequence is a min max theorem for a continuous real valued function on a product of finite dimensional compact convex bodies where the usual min and max sections are no longer required to be either convex or acyclic.

Mathematical Subject Classification 2000

Primary: 55C20

Secondary: 54H25

Milestones

Received: 24 November 1971

Revised: 18 August 1972

Published: 1 April 1973