Stability of the fixed point property and universal maps

Sanjurjo, José M. R.

doi:10.1090/S0002-9939-1989-0931746-X

Stability of the fixed point property and universal maps
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by José M. R. Sanjurjo PDF

Proc. Amer. Math. Soc. 105 (1989), 221-230 Request permission

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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Sur un probleme de MM. Kuratowski et Ulam

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