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On the Complete Invariance Property in Some Uncountable Products

Published online by Cambridge University Press:  20 November 2018

Piotr Koszmider
Piotr Koszmider*
Affiliation:
Department of Mathematics University of Toronto Toronto, Ontario, Canada M5S1A1. koszmider@math. toronto. edu
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Abstract

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We consider uncountable products of nontrivial compact, convex subsets of normed linear spaces. We show that these products do not have the complete invariance property i.e. they include a nonempty, closed subset which is not a fixed point set (i.e. the set of all fixed points) for any continuous mapping from the product into itself. In particular we give an answer to W.Weiss' question whether uncountable powers of the unit interval have the complete invariance property.

Keywords

54H25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 2 , 01 June 1992 , pp. 221 - 229
Copyright
Copyright © Canadian Mathematical Society 1992 

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