Fixed point sets of products and cones

Academic Article

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. © 1982, University of California, Berkeley. All Rights Reserved.
  • Authors

    Published In

    Digital Object Identifier (doi)

    Author List

  • Martin JR; Oversteegen LG; Tymchatyn ED
  • Start Page

  • 133
  • End Page

  • 139
  • Volume

  • 101
  • Issue

  • 1