| Title:
|
Multifibrations. A class of shape fibrations with the path lifting property (English) |
| Author:
|
Giraldo, Antonio |
| Author:
|
Sanjurjo, Jose M. R. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
29-38 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
shape fibration |
| Keyword:
|
multivalued map |
| Keyword:
|
path lifting property |
| Keyword:
|
strong shape |
| MSC:
|
54C56 |
| MSC:
|
55P55 |
| MSC:
|
55R05 |
| idZBL:
|
Zbl 1079.55503 |
| idMR:
|
MR1814629 |
| . |
| Date available:
|
2009-09-24T10:39:23Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127623 |
| . |
| Reference:
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