Spaces which Invert Weak Homotopy Equivalences
It is well known that if X is a CW-complex, then for every weak homotopy equivalence f : A → B, the map f: [X, A] → [X, B] induced in homotopy classes is a bijection. In fact, up to homotopy equivalence, only CW-complexes have that property. Now, for which spaces X is f: [B, X] → [A, X] a bijection...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/88608 |
| Acceso en línea: | http://hdl.handle.net/11336/88608 |
| Access Level: | acceso embargado |
| Palabra clave: | HOMOTOPY TYPES NON-HAUSDORFF SPACES WEAK HOMOTOPY EQUIVALENCES https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | It is well known that if X is a CW-complex, then for every weak homotopy equivalence f : A → B, the map f: [X, A] → [X, B] induced in homotopy classes is a bijection. In fact, up to homotopy equivalence, only CW-complexes have that property. Now, for which spaces X is f: [B, X] → [A, X] a bijection for every weak equivalence f? This question was considered by J. Strom and T. Goodwillie. In this note we prove that a non-empty space inverts weak equivalences if and only if it is contractible. |
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