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Rodríguez Sanjurjo, José Manuel
(1990)
*Shape morphisms and small multivalued maps.*
Mathematica Japonica, 35
(4).
pp. 713-717.
ISSN 0025-5513

Official URL: http://www.jams.or.jp/notice/mj/mj.html

URL | URL Type |
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http://www.jams.or.jp/ | Organisation |

## Abstract

An upper semicontinuous multivalued map F:X→Y is said to be ε -small if the diameter of F(x) is less than ε for each x∈X . F and G are ε -homotopic if there is an ε -small homotopy H:X×I→Y joining F and G . F:X×[0,∞)→Y is a fine multivalued map if for each ε>0 there is m≥0 such that F|X×[m,∞) is ε -small. Fine multivalued maps F,G:X×[0,∞)→Y are homotopic provided for each ε>0 there is m≥0 such that F|X×[m,∞) is ε -homotopic to G|X×[0,∞) . The main result of the paper is to show a bijective correspondence between shape morphisms from X to Y , X and Y being compact metrizable, and homotopy classes of fine multivalued maps from X×[0,∞) to Y .

Item Type: | Article |
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Uncontrolled Keywords: | shape theory; multivalued maps; metric compacta; fine multivalued map; shape morphism; |

Subjects: | Sciences > Mathematics > Topology |

ID Code: | 21937 |

Deposited On: | 19 Jun 2013 16:10 |

Last Modified: | 12 Dec 2018 15:13 |

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