Polyhedron-like continua without the fixed-point property
by
Charles L. Hagopian
California State University, Sacramento

Let K be a locally-connected continuum that contains an open subset homeomorphic to euclidean n-space for some integer n > 1. A continuum M is K-like if for each positive real number \epsilon, there exists an \epsilon-map of M onto K. We prove that every tree-like continuum is K-like. Hence D. P. Bellamy's elegant example without the fixed-point property is a K-like continuum. This result answers J. Segal and T. Watanabe's fixed-point question for complex projective space-like continua. It also shows that a recent fixed-point theorem of M. M. Marsh for real projective space-like continua is sharp. In particular, there exist projective plane-like continua without the fixed-point property.

Date received: January 25, 2002