An intrinsic description of shape
| dc.contributor.author | Rodríguez Sanjurjo, José Manuel | |
| dc.date.accessioned | 2023-06-20T17:03:18Z | |
| dc.date.available | 2023-06-20T17:03:18Z | |
| dc.date.issued | 1992-02 | |
| dc.description.abstract | We give in this paper a description of the shape category of compacta in terms of multivalued maps. We introduce the notion of a multi-net and prove that the shape category of compacta is isomorphic to the category HN whose objects are metric compacta and whose morphisms are homotopy classes of multi-nets. This description is intrinsic in the sense that it does not make use of external elements such as ANR-expansions or embeddings in appropriate AR-spaces. We present many applications of this new formulation of shape. | |
| 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/17048 | |
| dc.identifier.doi | 10.2307/2153955 | |
| dc.identifier.issn | 0002-9947 | |
| dc.identifier.officialurl | http://www.ams.org/journals/tran/1992-329-02/S0002-9947-1992-1028311-X/S0002-9947-1992-1028311-X.pdf | |
| dc.identifier.relatedurl | http://www.ams.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57695 | |
| dc.issue.number | 2 | |
| dc.journal.title | Transactions of the American Mathematical Society | |
| dc.language.iso | eng | |
| dc.page.final | 636 | |
| dc.page.initial | 625 | |
| dc.publisher | American Mathematical Society | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 514 | |
| dc.subject.cdu | 515.1 | |
| dc.subject.keyword | Small multivalued map | |
| dc.subject.keyword | multi-net | |
| dc.subject.keyword | simple multi-net | |
| dc.subject.keyword | approximative map | |
| dc.subject.keyword | refinable map | |
| dc.subject.keyword | strong shape equivalence | |
| dc.subject.keyword | internal movability. | |
| dc.subject.ucm | Geometría | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1204 Geometría | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | An intrinsic description of shape | |
| dc.type | journal article | |
| dc.volume.number | 329 | |
| dcterms.references | S. Bogatyi, Approximate and fundamental retracts, Math. Sb. 22 (1974), 91-103. K. Borsuk, Theory of retracts, Monogr. Mat. 44, Polish Scientific Publishers, Warszawa, 1967. _, Concerning homotopy properties of compacta, Fund. Math. 62 (1968), 223-254. _, Theory of shape, Monogr. Mat. 59, Polish Scientific Publishers, Warszawa, 1975. _, Some quantitative properties of shapes, Fund. Math. 93 (1976), 197-212. J. Dydak, On internally movable compacta, Bull. Acad. Polon. Sei. 27 (1979), 107-110. J. Dydak and J. Segal, Shape theory: An introduction, Lecture Notes in Math., vol. 688, Springer-Verlag, Berlin, 1978. _, Strong shape theory, Dissertationes Math. 192 (1981), 1-42. J. E. Felt, e-continuity and shape, Proc. Amer. Math. Soc. 46 (1974), 426-430. H. Kato, Refinablem aps in the theory of shape, Fund. Math. 113 (1981), 119-129. V. L. Klee and A. Yandl, Some proximate concepts in topology, Symposia Math., vol. 16 (INDAM, Rome, 1973), Academic Press, London, 1974, pp. 21-39. V. F. Laguna and J. M. R. Sanjurjo, Internal fundamental sequences and approximative retracts, Topology Appl. 17 (1984), 189-197. _, Spaces of approximative maps, Math. Japon. 31 (1986), 623-633. _, Shape morphisms and spaces of approximative maps, Fund. Math. 183 (1989), 225-235. S. Mardesic, On Borsuk's shape theory for compact pairs, Bull. Acad. Polon. Sei. 21 (1973), 1131-1136. S. Mardesic and J. Segal, Shapes of compacta and ANR-systems, Fund. Math. 72 (1971), 41-59. _, Shape theory, North-Holland, Amsterdam, 1982. M. A. Moron, On internal movability, internal shape and internal MANR-spaces, Colloq. Math, (to appear). J. M. R. Sanjurjo, On limits of shape maps, Topology Appl. 23 (1986), 173-181. _, A non-continuous description of shape, Quart. J. Math. Oxford Ser. 40 (1989), 351-359. _, Shape morphisms and small multivalued maps, preprint. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | f54f1d9d-37e9-4c15-9d97-e34a6343e575 | |
| relation.isAuthorOfPublication.latestForDiscovery | f54f1d9d-37e9-4c15-9d97-e34a6343e575 |
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