### Impacto

Giraldo, A. and Rodríguez Sanjurjo, José Manuel
(2001)
*Multifibrations. A class of shape fibrations with the path lifting property.*
Czechoslovak Mathematical Journal , 51
(1).
pp. 29-38.
ISSN 1572-9141

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## Abstract

In this paper we introduce a class of maps possessing a multivalued homotopy lifting property with respect to every topological space. We call these maps multifibrations and they represent a formally stronger concept than that of shape fibration. Multifibrations have the interesting property of being characterized in a completely intrinsic. way by a path lifting property involving only the total and the base space of the fibration. We also show that multifibrations land also, with some restrictions, shape fibrations) have a lifting property for homotopies of fine multivalued maps. This implies, when the spaces considered are metric compacta, that the possibility of lifting a fine multivalued map is a property of the corresponding strong shape morphism and not of the particular map considered.

Item Type: | Article |
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Uncontrolled Keywords: | shape fibration, multivalued map, path liftingp roperty, strong shape |

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

ID Code: | 16878 |

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Deposited On: | 25 Oct 2012 09:29 |

Last Modified: | 07 Feb 2014 09:37 |

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