Original scientific paper

HYPERSPACES OF H-CLOSED SPACES

Ivan Lončar

Abstract

HYPERSPACES OF H-CLOSED SPACES
Let X be a topological space. By Exp(X) we denote the set of all closed subset of X with the Vietoris topology. The properties of Exp(X) in the case of compact X are wellknown. For proving the analogous properties of Exp(X) for H-closed X we firstly generalize
Alexander's lema for H-closed and for nearly compact spaces. For this purpose the notion of n ~ subbase is introduced.
In Section Two we prove that the subbase of exponential topology is P) - subbase (Lemma 2.8.). The Alexander's lema is generaUzed in Theorem 2.9. Finally, the main Theorem of this Section (Theorem 2.10.) i.e. theorem "X is QHC iff Exp(X) is QHC" is proved. Let us recal that X is QHC if each open cover t/ of X has a finite subfamily
{Ui,...,Un} such that X = CI Ui fl ••• fl CI Un. Section Three contains the analogous theorems on Exp(X) for nearly compact spaces
(Theorems 3.4. and 3.6.).

Keywords

Hrčak ID:

134070

URI

https://hrcak.srce.hr/134070

Publication date:

5.12.1989.

Article data in other languages: croatian

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