On weak normality of space \(X^ 2\smallsetminus\Delta\)
type: Item
instance of: scholarly article
title: On weak normality of space \(X^ 2\smallsetminus\Delta\)
zbMATH Open document ID: 0878.54010
published in: Moscow University Mathematics Bulletin
publication date: 1997-07-13T00:00:00Z
review text: \textit{A. V. Arkhangel'skij} and the author proved [Topology Appl. 35, 121-126 (1990; Zbl 0707.54018)] that a compact space \(X\) is first-countable provided that \(X^2\smallsetminus\Delta\) is normal. In this paper the author shows that normality can be replaced by a weaker separation property. Namely, one can merely assume that any two disjoint closed subsets of \(X^2\smallsetminus\Delta\) can be separated, i.e., mapped to disjoint sets by a continuous function of \(X^2\smallsetminus\Delta\) into a metrizable space.
Mathematics Subject Classification ID: 54D15
Mathematics Subject Classification ID: 54B10
zbMATH DE Number: 1028761
zbMATH Keywords: weakly normal
zbMATH Keywords: first countable
author: Anatoli P. Kombarov
reviewed by: Jozef Chaber
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1028761