Density and finiteness. A discrete approach to shape
| dc.contributor.author | Giraldo, A. | |
| dc.contributor.author | Rodríguez Sanjurjo, José Manuel | |
| dc.date.accessioned | 2023-06-20T17:02:19Z | |
| dc.date.available | 2023-06-20T17:02:19Z | |
| dc.date.issued | 1997-03 | |
| dc.description.abstract | We show in this paper that the category of shape can be modelled in discrete terms using maps defined in dense subsets of compacta. This approach to shape provides in addition a characterization of the shape of compacta which does not require external elements and uses only continuous single-valued functions, in contrast with the existing internal characterizations of shape. As an application, we prove a connection between the notion of shape image, due to Lisica, and the basic notion of omega limit of a dynamical system. | |
| 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/16962 | |
| dc.identifier.doi | 10.1016/S0166-8641(97)00098-9 | |
| dc.identifier.issn | 0166-8641 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0166864197000989 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57668 | |
| dc.issue.number | 1 | |
| dc.journal.title | Topology and its Applications | |
| dc.language.iso | eng | |
| dc.page.final | 77 | |
| dc.page.initial | 61 | |
| dc.publisher | Elsevier Science | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 514 | |
| dc.subject.cdu | 515.1 | |
| dc.subject.keyword | Density: Discrete map: Shape category | |
| dc.subject.keyword | Shape image: Omega limit: Lyapunov stability | |
| dc.subject.ucm | Geometría | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1204 Geometría | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | Density and finiteness. A discrete approach to shape | |
| dc.type | journal article | |
| dc.volume.number | 76 | |
| dcterms.references | N.P. Bhatia and G.P. Szego, Stability theory of dynamical systems, Grundlehren Math. Wiss. 161 (Springer, Berlin, 1970). K. Borsuk, Concerning homotopy properties of compacta, Fund. Math. 62 (1968) 223-254. K. Borsuk, On movable compacta, Fund. Math. 66 (1969) 137-146. K. Borsuk, Theory of Shape. Monogratie Matematyczne 59 (Polish Scientitic Publishers, Warszawa, 1975). Z. Cerin. Shape theory intrinsically. Publ. Mat. 37 (1993) 317-334. Z. Cerin. Proximate topology and shape theory, Proc. Roy. Sot. Edinburgh I25 (1995) 595-615. Z. Cerin. Equivariant shape theory, Math. Proc. Cambridge Philos. Sot. I I7 (1995) 303-320. J.M. Cordier and T. Porter, Shape Theory. Categorical Methods of Approximation, Ellis Horwood Series: Mathematics and its Applications (Ellis Horwood, Chichester, 1989). J. Dydak and J. Segal. Shape Theory: An Introduction, Lecture Notes in Math. 688 (Springer, Berlin, 1978). J. Dydak and J. Segal, A list of open problems in shape theory, in: J. van Mill and G.M. Reed. eds., Open problems in Topology (North-Holland, Amsterdam. 1990) 457-467. J.E. Felt, E-continuity and shape, Proc. Amer. Math. Sot. 46 (1974) 426430. R.H. Fox, On shape. Fund. Math. 74 ( 1972) 47-7 I. A. Giraldo and J.M.R. Sanjurjo, Strong multihomotopy and Steenrod loop spaces, J. Math. Sot. Japan 47 (1995) 475489. B. Gunther and J. Segal. Every attractor of a flow on a manifold has the shape of a finite polyhedron, Proc. Amer. Math. Sot. I I9 (1993) 321-329. R.W. Kieboom. An intrinsic characterization of the shape of paracompacta by means of noncontinuous single-valued maps. Bull. Belg. Math. Sot. I (1994) 701-71 I. J.T. Lisica, Strong shape theory and multivalued maps, Glas. Mat. I8 (1983) 371-382. S. MardeSic and J. Segal, Shapes of compacta and ANR-systems, Fund. Math. 72 (197 I) 31-59. S. MardeSii- and J. Segal. Equivalence of the Borsuk and the ANR-system approach to shapes. Fund. Math. 72 (1971) 61-68. S. MardeSiC and J. Segal. Shape Theory (North-Holland. Amsterdam, 1982). M.A. Moron and F.R. Ruiz del Portal. Multivalued maps and shape for paracompacta. Math. Japon. 39 (1994) 489-500. M.A. Moron and F.R. Ruiz de1 Portal, Shape as a Cantor completion process, Math. Z., to appear. P. Mrozik. Some applications of lattice theory to shape theory. Arch. Math. 47 ( 1986) 243-250. J.M.R. Sanjurjo. A non-continuous description of the shape category of compacta, Quart. J. Math. Oxford (2) 40 (1989) 35 1-359. 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. Sot. 329 (1992) 625-636. J.M.R. Sanjurjo. Multihomotopy, Tech spaces of loops and shape groups, Proc. London Math. Sot. (3) 69 (1994) 330-344. J.M.R. Sanjurjo, On the structure of uniform attractors, J. Math. Anal. Appl. I52 (1995) 519-528. P. Saperstone. Semidynamical Systems in Infinite Dimensional Spaces. Appl. Math. Sci. 37 (Springer. Berlin. I98 I ). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | f54f1d9d-37e9-4c15-9d97-e34a6343e575 | |
| relation.isAuthorOfPublication.latestForDiscovery | f54f1d9d-37e9-4c15-9d97-e34a6343e575 |
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