Generalization of \(G^*_\delta\)-diagonals and \(w\Delta\)-spaces
type: Item
instance of: scholarly article
title: Generalization of \(G^*_\delta\)-diagonals and \(w\Delta\)-spaces
zbMATH Open document ID: 0909.54021
DOI: 10.1023/A:1006586206579
published in: Acta Mathematica Hungarica
publication date: 1999-03-14T00:00:00Z
review text: The concept of \(G^*_\delta\)-diagonal spaces as a generalization of metric spaces is the subject of additional generalization to the concept of quasi-\(G^*_\delta\)-diagonal and quasi-\(w\Delta\)-spaces. The quasi-\(w\Delta\)-space concept is in fact the generalization of \(w\Delta\)-space concept. It is shown that a quasi-Moore space can be characterized in terms of these concepts introduced by the author. As a consequence the following metrization theorems are proved: 1. Every paracompact \(w\Delta\)-space with quasi-\(G^*_\delta\)-diagonal is metrizable. 2. Every collectionwise normal \(\delta\) quasi-\(w\Delta\)-space is metrizable. The main result is the following extension of Hodel's theorem: A space is a quasi-Moore space if and only if it is regular quasi-\(w\Delta\)-space with quasi-\(G^*_\delta\)-diagonal. A space is developable if and only if it is a perfect, quasi-\(w\Delta\)-space with a quasi-\(G^*_\delta\)-diagonal. The complete clarification of relationships between the classes of developable spaces, \(w\Delta\)-spaces, quasi-developable spaces, perfect spaces, quasi-\(w\Delta\)-spaces and quasi-\(G^*_\delta\)-diagonal spaces are also given.
Mathematics Subject Classification ID: 54D80
Mathematics Subject Classification ID: 54E30
zbMATH DE Number: 1261216
zbMATH Keywords: Moore space
zbMATH Keywords: developable space
zbMATH Keywords: \(w\)-space
zbMATH Keywords: perfect space
zbMATH Keywords: quasi \(w\)-space
zbMATH Keywords: quasi-\(G\)-diagonal
zbMATH Keywords: metrizable space
zbMATH Keywords: metrization theorem
author: A. Mohamad
reviewed by: Jiří Vaníček
MaRDI profile type: Publication
full work available at URL: a:1006586206579
OpenAlex ID: W1709818029
description: scientific article; zbMATH DE number 1261216