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Stability of the fixed-point property and universal maps

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Rodríguez Sanjurjo, José Manuel (1989) Stability of the fixed-point property and universal maps. Proceedings of the American Mathematical Society, 105 (1). pp. 221-230. ISSN 0002-9939

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Official URL: http://www.ams.org/journals/proc/1989-105-01/S0002-9939-1989-0931746-X/S0002-9939-1989-0931746-X.pdf


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Abstract

In this interesting paper, the author gives a stability condition for the fixed point property in terms of K. Borsuk's fundamental metric on a hyperspace of a compact metric space. This condition is equivalent to that originally given by V. L. Klee [Colloq. Math. 8 (1961), 43–46] but it reflects richer properties. By replacing exact conditions with their proximate analogues, the author introduces a notion of proximately universal maps and studies many of their properties. In particular, he investigates their preservation under composition with weakly refinable and refinable maps to get improvements of results of E. E. Grace [Proc. Amer. Math. Soc. 98 (1986), no. 2, 329–335] and C. W. Ho [Fund. Math. 111 (1981), no. 2, 169–177].


Item Type:Article
Uncontrolled Keywords:Fixed-point and coincidence theorems; Weak and generalized continuity; Shape theory
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:17126
Deposited On:16 Nov 2012 09:53
Last Modified:12 Dec 2018 15:13

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