Cones that are 1/2-homogeneous
A space is 1/2-homogeneous provided that there are exactly two orbits for the action of 2 the group of homeomorphisms of the space onto itself. Let X be a nonempty compact metric space such that the cone over X is 1/2-homogeneous. It is shown that if X is finite-dimensional, then X is an absolute ne...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2007 |
| País: | México |
| Institución: | Universidad Nacional Autónoma de México |
| Repositorio: | Sistema de Información de la Facultad de Ciencias, UNAM |
| OAI Identifier: | oai:repositorio.fciencias.unam.mx:11154/1167 |
| Acceso en línea: | http://hdl.handle.net/11154/1167 |
| Access Level: | acceso abierto |
| Palabra clave: | Mathematics absolute (neighborhood) retract arc arc-like atriodic circle-like cone connected im Kleinen contimuum contractible dendrite dimension finite graph Hilbert cube homogeneous 1/2-homogeneous 1/n-homogeneous homotopically labile point homotop |
| Sumario: | A space is 1/2-homogeneous provided that there are exactly two orbits for the action of 2 the group of homeomorphisms of the space onto itself. Let X be a nonempty compact metric space such that the cone over X is 1/2-homogeneous. It is shown that if X is finite-dimensional, then X is an absolute neighborhood retract. A general theorem is proved which shows that finite dimensionality is necessary. It is shown that if X is a 1-dimensional continuum or if X does not contain certain types of triods in some nonempty open set, then X is an arc or a simple closed curve (assuming Cone(X) is 1/2-homogeneous). A number of corollaries are derived. Some unanswered questions are stated. |
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