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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Stability of the fixed point property and universal maps

Author: José M. R. Sanjurjo
Journal: Proc. Amer. Math. Soc. 105 (1989), 221-230
MSC: Primary 54H25; Secondary 54C08, 54F43
MathSciNet review: 931746
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Abstract: We give a stability condition for the fixed point property in terms of the fundamental metric and the metric of continuity introduced by K. Borsuk. This condition is equivalent to that originally given by V. Klee but reflects richer properties. We introduce the notion of a proximately universal map and study many of its properties. Relationships among proximately universal maps and some generalized refinable maps introduced by E. E. Grace are studied. In particular we prove that every weakly refinable map $ r:X \to Y$ is proximately universal whenever $ X$ has the proximate fixed point property. This generalizes a result of Grace.

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Keywords: Proximate fixed point property, refinable map, weakly refinable map, proximately universal map
Article copyright: © Copyright 1989 American Mathematical Society

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