1. Multifibrations. A class of shape fibrations with the path lifting property
- Creator:
- Giraldo, Antonio and Sanjurjo, José M. R.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- shape fibration, multivalued map, path lifting property, and strong shape
- Language:
- English
- Description:
- 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 (and 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public