Alpha-paracompact subsets and well-situated subsets

  1. Francisco Gallego Lupiáñez 1
  1. 1 Universidad Complutense de Madrid
    info

    Universidad Complutense de Madrid

    Madrid, España

    ROR 02p0gd045

Revista:
Czechoslovak Mathematical Journal

ISSN: 1572-9141

Año de publicación: 1988

Volumen: 38

Número: 2

Páginas: 191-197

Tipo: Artículo

GOOGLE SCHOLAR lock_openDocta Complutense editor

Otras publicaciones en: Czechoslovak Mathematical Journal

Resumen

In this paper -paracompact and well-situated subsets are further examined. A subset E of a space X is -paracompact if every covering of E by open sets has a refinement by open sets, locally finite in X, which covers E [C. E. Aull, Proc. 2nd Prague Topol.Symp. 1966, 45-51 (1967; Zbl 0162.264)] and is well-situated in X if for every paracompact T2 space Y, E × Y is -paracompact in X × Y [H. W. Martin, Topology Appl.12, 305-313 (1981; Zbl 0483.54011)]. Covering properties of -paracompact and wellsituated ubsets are obtained, -paracompact and well-situated subsets are characterizedin regular spaces, the behavior of paracompact and well-situated subsets under perfect mappings is studied, and it is shown that the class of all paracompact T2 spaceswhich are well-situated in every paracompact T2 space in which they are embedded as closed subsets, is perfect.