The fixed point property in every weak homotopy type
We prove that for any connected compact CW-complex K there exists aspace X weak homotopy equivalent to K which has the fixed point property, that is,every continuous map X -> X has a fixed point. The result is known to be false if werequire X to be a polyhedron. The space X we construct is a non-...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2016 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/18909 |
| Acceso en línea: | http://hdl.handle.net/11336/18909 |
| Access Level: | acceso abierto |
| Palabra clave: | FIXED POINT PROPERTY SIMPLICIAL COMPLEXES WEAK HOMOTOPY TYPES FINITE TOPOLOGICAL SPACES https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | We prove that for any connected compact CW-complex K there exists aspace X weak homotopy equivalent to K which has the fixed point property, that is,every continuous map X -> X has a fixed point. The result is known to be false if werequire X to be a polyhedron. The space X we construct is a non-Hausdorff space withfinitely many points. |
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