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
Publication date:
5.12.1989.
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