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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Detalles Bibliográficos
Autor: Charatonik, WJ
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
Descripción
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.