Fixed point set of products and cones

John Rowlay Martin, Lex Gerard Oversteegen and Edward D. Tymchatyn

Vol. 101 (1982), No. 1, 133–139

DOI: 10.2140/pjm.1982.101.133

Abstract

A space X is said to have the complete invariance property (CIP) if every nonempty closed subset of X is the fixed point set of some self-map of X. Examples are given to show that for the class of locally connected continua, the operations of taking products, cones, and strong deformation retractions need not preserve CIP. In fact, it is shown that the operations of taking products and cones do not preserve CIP for LC^∞ continua.

Mathematical Subject Classification 2000

Primary: 54F20, 54F20

Secondary: 54H25

Milestones

Received: 15 May 1981

Published: 1 July 1982