Concerning ultraparacompact spaces

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

    Universidad Complutense de Madrid

    Madrid, España

    ROR 02p0gd045

Revista:
Questions and answers in general topology

ISSN: 0918-4732

Año de publicación: 1993

Volumen: 11

Número: 2

Páginas: 145-152

Tipo: Artículo

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Otras publicaciones en: Questions and answers in general topology

Resumen

In this interesting paper a new class of ultraparacompact spaces, the class of so-called (P*) spaces, is introduced and investigated. A zero-dimensional Hausdorff space is called a (P*) space if for every open cover and for every clopen base such that every finite union of elements of the base can be partitioned into elements of the base, there exists a discrete refinement consisting of members of the base. For example, a zero-dimensional dense subspace of Rn is a (P*) space. The authors provide a characterization of the (P*) property and show that every ultraparacompact C-scattered space satisfies property (P*). At the end of the paper some open questions are raised.