Multifibrations. A class of shape fibrations with the path lifting property
| dc.contributor.author | Giraldo, A. | |
| dc.contributor.author | Rodríguez Sanjurjo, José Manuel | |
| dc.date.accessioned | 2023-06-20T17:01:52Z | |
| dc.date.available | 2023-06-20T17:01:52Z | |
| dc.date.issued | 2001 | |
| dc.description.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. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/16878 | |
| dc.identifier.doi | 10.1023/A:1013793418931 | |
| dc.identifier.issn | 1572-9141 | |
| dc.identifier.officialurl | http://www.springerlink.com/content/ur58kq2855685173/fulltext.pdf | |
| dc.identifier.relatedurl | http://www.springerlink.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57655 | |
| dc.issue.number | 1 | |
| dc.journal.title | Czechoslovak Mathematical Journal | |
| dc.language.iso | eng | |
| dc.page.final | 38 | |
| dc.page.initial | 29 | |
| dc.publisher | Mathematical Institute of the Academy of Sciences of the Czech Republic | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 514 | |
| dc.subject.cdu | 515.1 | |
| dc.subject.keyword | shape fibration | |
| dc.subject.keyword | multivalued map | |
| dc.subject.keyword | path liftingp roperty | |
| dc.subject.keyword | strong shape | |
| dc.subject.ucm | Geometría | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1204 Geometría | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | Multifibrations. A class of shape fibrations with the path lifting property | |
| dc.type | journal article | |
| dc.volume.number | 51 | |
| dcterms.references | K. Borsuk: On movable compacta. Fund. Math. 66 (1969), 137–146. K. Borsuk: Theory of Shape (Monografie Matematyczne 59). Polish Scientific Publishers, Warszawa, 1975. F.W.Cathey: Shape fibrations and strongs hape theory. Topology Appl. 14 (1982), 13–30. Z . Čerin: Shape theory intrinsically. Publ. Mat. 37 (1993), 317–334. Z . Čerin: Proximate topology and shape theory. Proc. Roy. Soc. Edinburgh 125 (1995), 595–615. Z . Čerin: Approximate fibrations. To appear. D. Coram and P. F. Duvall, Jr.: Approximate fibrations. Rocky Mountain J. Math. 7 (1977), 275–288. J.M.Cordier and T. Porter: Shape Theory. Categorical Methods of Approximation (Ellis Horwood Series: Mathematics and its Applications). Ellis Horwood Ltd., Chichester, 1989. J. Dydak and J. Segal: Shape Theory: An Introduction (Lecture Notes in Math. 688). Springer-Verlag, Berlin, 1978. J. Dydak and J. Segal: A list of open problems in shape theory. J.Van Mill and G. M.Reed: Open problems in Topology. North Holland, Amsterdam, 1990, pp. 457–467. J. E. Felt: ε-continuity and shape. Proc. Amer. Math. Soc. 46 (1974), 426–430. A. Giraldo: Shape fibrations, multivalued maps and shape groups. Canad. J. Math 50 (1998), 342–355. A. Giraldo and J. M. R. Sanjurjo: Strongm ultihomotopy and Steenrod loop spaces. J. Math. Soc. Japan. 47 (1995), 475–489. R.W. Kieboom: An intrinsic characterization of the shape of paracompacta by means of non-continuous single-valued maps. Bull. Belg. Math. Soc. 1 (1994), 701–711. K. Kuratowski: Topology I. Academic Press, New York, 1966. S. Mardešic: Approximate fibrations and shape fibrations. Proc. of the International Conference on Geometric Topology. PWN, Polish Scientific Publishers, 1980, pp. 313–322. S. Mardešic and T.B.Rushing: Shape fibrations. General Topol. Appl. 9 (1978), 193–215. S. Mardešic and T.B.Rushing: Shape fibrations II. Rocky Mountain J. Math. 9 (1979), 283–298. S. Mardešic and J. Segal: Shape Theory. North Holland, Amsterdam, 1982. E.Michael: Topologies on spaces of subsets. Trans. Amer. Math. Soc. 71 (1951), 152–182. M. A.Morón and F. R.Ruiz del Portal: Multivalued maps and shape for paracompacta. Math. Japon. 39 (1994), 489–500. J. M. R. Sanjurjo: A non-continuous description of the shape category of compacta. Quart. J. Math. Oxford (2) 40 (1989), 351–359. J. M. R. Sanjurjo: Multihomotopy sets and transformations induced by shape. Quart. J. Math. Oxford (2) 42 (1991), 489–499. J. M. R. Sanjurjo: An intrinsic description of shape. Trans. Amer. Math. Soc. 329 (1992), 625–636. J. M. R. Sanjurjo: Multihomotopy, Čech spaces of loops and shape groups. Proc. London Math. Soc. (3) 69 (1994), 330–344. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | f54f1d9d-37e9-4c15-9d97-e34a6343e575 | |
| relation.isAuthorOfPublication.latestForDiscovery | f54f1d9d-37e9-4c15-9d97-e34a6343e575 |
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