Vol. 101, No. 1, 1982

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Fixed point set of products and cones

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

Vol. 101 (1982), No. 1, 133–139

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
Received: 15 May 1981
Published: 1 July 1982
John Rowlay Martin
Lex Gerard Oversteegen
Edward D. Tymchatyn