On weak shape equivalences
We prove that weak shape equivalences are monomorphisms in the shape category of uniformly pointed movable continua Sh(M). We use an example of Draper and Keesling to show that weak shape equivalences need not be monomorphisms in the shape category. We deduce that Sh(M) is not balanced. We give a ch...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 1999 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/57320 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/57320 |
| Access Level: | acceso abierto |
| Palabra clave: | 515.143 Homotopy Monomorphisms Epimorphisms Weak shape equivalence Shape category of uniformly pointed movable continua Monomorphisms and epimorphisms in categories Topología 1210 Topología |
| Sumario: | We prove that weak shape equivalences are monomorphisms in the shape category of uniformly pointed movable continua Sh(M). We use an example of Draper and Keesling to show that weak shape equivalences need not be monomorphisms in the shape category. We deduce that Sh(M) is not balanced. We give a characterization of weak dominations in the shape category of pointed continua, in the sense of Dydak (1979). We introduce the class of pointed movable triples (X,F,Y), for a shape morphism F:X --> Y, and we establish an infinite-dimensional Whitehead theorem in shape theory from which we obtain, as a corollary, that for every pointed movable pair of continua (Y,X) the embedding j: X --> Y is a shape equivalence iff it is a weak shape equivalence. |
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