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

Antonio Giraldo; José M. R. Sanjurjo

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 1, page 29-38
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Giraldo, Antonio, and Sanjurjo, José M. R.. "Multifibrations. A class of shape fibrations with the path lifting property." Czechoslovak Mathematical Journal 51.1 (2001): 29-38. <http://eudml.org/doc/30611>.

@article{Giraldo2001,
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 (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.},
author = {Giraldo, Antonio, Sanjurjo, José M. R.},
journal = {Czechoslovak Mathematical Journal},
keywords = {shape fibration; multivalued map; path lifting property; strong shape; shape fibration; multivalued map; path lifting property; strong shape},
language = {eng},
number = {1},
pages = {29-38},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Multifibrations. A class of shape fibrations with the path lifting property},
url = {http://eudml.org/doc/30611},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Giraldo, Antonio
AU - Sanjurjo, José M. R.
TI - Multifibrations. A class of shape fibrations with the path lifting property
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 1
SP - 29
EP - 38
AB - 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.
LA - eng
KW - shape fibration; multivalued map; path lifting property; strong shape; shape fibration; multivalued map; path lifting property; strong shape
UR - http://eudml.org/doc/30611
ER -

References

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