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Se introducen las nociones  de conjunto ω-cerrado, funcion ω-cerrada y espacio P*, generalizando las de conjunto cerrado, función cerrada y espacio P donde todo Gδ es abierto, respectivamente. Se demuestra que las imágenes inversas de funciones continuas ω-cerradas preservan a La propiedad de Lindelöf en caso de que cada fibra sea Lindelöf, b paracompacidad para compacidad fuerte si el dominio es regular y cada fibra es relativamente paracompacta Lindelöf . Si X es Lindelöf  y Y es un espacio P*, entonces la proyección XxY→ Y es ω-cerrada y por tanto: XxYes Lindelöf  paracompacto, fuertemente paracompacto sí y sólamente si Y lo es., In this paper the concepts of ω-closed set, ω-closed mapping and P*-spaces are defined and the following are the main results: a Let f be a continuous ω-closed mapping of a space X onto a space Y such that f-1y is Lindelöf for each Y in Y. Then X is Lindelöf if Y is so. b Let f be a continuous ω-closed mapping of a regular space X onto a space Y. Then X is paracompact strongly paracompact if Y is paracompact strongly paracompact and for each y in Y, f-1y is paracompact relative to X Lindelöf . c Let X be a Lindelöf  space and Y be a P*-space, then the projection P:Xxy Y is an ω-closed mapping. Hence, XxY is Lindelöf paracompact, strongly paracompact if and only if Y is so.

Tipo de documento: Artículo - Article

Palabras clave: Notions of set; function, epsacio; Lindelöf property; paracompacta, Nociones de conjunto; funcion, epsacio; propiedad de Lindelöf; paracompacta





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Rev~ta Cotomb~na de Mat~~~ vat.
XVI (1982) pag~.
65 - 78 w-CLOSED MAPPINGS * by H.Z.
HDEIB ABSTRACT.
In this paper the concepts ofw-closed set, w-closed mapping and P*-spaces are defined and the following are the main results: (a) Let f be a continuous w-closed mapping of a space X onto a space Y such that f-1(y) is Lindelof for each Y in Y.
Then X is Lindelof if Y is so.
(b) Let f be a continuous w-closed mapping of a regular space X onto a space Y. Then X is paracompact (strongly paracompact) if Y is paracompact (strongly paracompact) and for each y in Y, f-1(y) is paracompact relative to X (L~ndelof). (c) Let X be a Lindelof space and Y be a pH-space, then the projection P:Xxy Y is an w-closed mapping. Hence, XxY is Lindelof (paracompact, strongly paracompact) if and only if Y is so. RESUMEN.
Se introducen las nociones 9.econjunto w-cerrado, funcion w-cerrada y espacio p-, generalizando las de conjunto cerrado, funcion cerrada y espacio P (donde todo Go es abierto), respectivamente. Se demuestra que las imagenes inversas de funciones continuas w-cerradas preservan (a) La propiedad de Lindelof en caso de que cada fibra sea Lindelof, * Part of this paper is extracted from the authors Ph.D. thesis, written at SUNY at Buffalo under the direction of Prof.
S.
Mrowka in February 1979. 65 (b) paracompacidad (paracompacidad fuerte) si el dominio es regular y cada fibra es relativamente paracompact~ (Lindelof).
Si X es Lindelof y Y es un espacio pH, entonces la proyecci6n xxy Y es w-cerrada y por tanto: Xxy es Lindelof (paracompacto, fuertemente paracompacto) si y s61amente si Y 10 es. 1. Introduction. In this paper we shall introduce a new kind of mappings, namely w-closed mappings, which are strictly weaker than closed mappings, then we show that the Lindelof property is preserved by counter images of w-closed mappings with Lindelof counter images of points. Also we show that the paracompactness (strong paracompactness) property is preserved by takin...





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