Fixed points in a class of sets

D. R. Smart

Vol. 23 (1967), No. 1, 163–165

DOI: 10.2140/pjm.1967.23.163

Abstract

THEOREM. A set of the form X = A ∪⋃ _i∈JB_i has the fixed point property if

(i) A is a closed simplex and each B_i is a closed simplex;

(ii) A ∩ B_i is a single point p_i for each i;

(iii) any arc in X joining a point in some B_i to a point in X − B_i must pass through p_i.

Mathematical Subject Classification

Primary: 54.85

Milestones

Received: 10 August 1966

Published: 1 October 1967