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Multifibrations. A class of shape fibrations with the path lifting property

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
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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