Openness and monotoneity of induced mappings
It is shown that for locally connected continuum X if the induced mapping C(f) : C(X) --> C(Y) is open,then f is monotone. As a corollary it follows that if the continuum X is hereditarily locally connected and C(f) is open, then f is a homeomorphism. An example is given to show that local connec...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 1999 |
| 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:11154/2151 |
| Acceso en línea: | http://hdl.handle.net/11154/2151 |
| Access Level: | acceso abierto |
| Palabra clave: | Mathematics, Applied Mathematics continuum hyperspace induced mapping open monotone |
| Sumario: | It is shown that for locally connected continuum X if the induced mapping C(f) : C(X) --> C(Y) is open,then f is monotone. As a corollary it follows that if the continuum X is hereditarily locally connected and C(f) is open, then f is a homeomorphism. An example is given to show that local connectedness is essential in the result. |
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