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

## 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 |
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Uncontrolled Keywords: | Fixed-point and coincidence theorems; Weak and generalized continuity; Shape theory |

Subjects: | Sciences > Mathematics > Geometry Sciences > Mathematics > Topology |

ID Code: | 17126 |

References: | K. Borsuk, Sur un problème de MM. Kuratowski et Ulam, Fund. Math. 31 (1938), 154-559. _, On a metrization of the hyperspace of a metric space, Fund. Math. 94 (1977), 191-207. _, On nearly extendable maps. Bull. Acad. Polon Sei. 23 (1975), 753-760. _, On the Lefschetz-Hopffixed point theorem for nearly extendable maps, Bull. Acad. Polon. Sei. 23 (1975), 1273-1279. Z. Cerin and A. P. Sostak, Some remarks on Borsuk ' s fundamental metric, Colloq. Math. Soc. Janos Bolyai, Budapest, 1978, pp. 233-252. M. H. Clapp, On a generalization of absolute neighborhood retracts, Fund. Math. 70 (1971), 117-130. J. Ford and J. W. Rogers, Jr., Refinable maps, Colloq. Math. 39 (1978), 263-269. E. E. Grace, Refinable maps and the proximate fixed point property. Topology Proc. 10 (1985), 293-303. _, Generalized refinable maps, Proc. Amer. Math. Soc. 98 (1986), 329-335. C. Ho, On a stability theorem for the fixed point property, Fund. Math. Ill (1981), 169-177. W. Holsztynski, Une généralisation du théorème de Brouwer sur les points invariants, Bull. Acad. Polon Sei. 12 (1964), 603-606. _, On the composition and products of universal mappings, Fund. Math. 64 (1969), 181- 188. V. L. Klee, Stability of the fixed point property, Colloq. Math. 8 (1961), 43-46. V. L. KJee and A. Yandl, Some proximate concepts in topology, Symposia Math. Publ. Inst. Naz. di Alta Matemática, Academic Press 16 (1974), 21-39. K. Kuratowski, Topology, Volume II, Academic Press, New York, PWN, Warszawa, 1968. C. W. Saalfrank, Neighborhood retraction generalized for compact Hausdorff spaces, Portugal Math. 20(1961), 11-16. |

Deposited On: | 16 Nov 2012 09:53 |

Last Modified: | 07 Feb 2014 09:42 |

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