On metrizability of paracompact \(p\)-spaces
type: Item
instance of: scholarly article
title: On metrizability of paracompact \(p\)-spaces
zbMATH Open document ID: 0881.54031
published in: Moscow University Mathematics Bulletin
publication date: 1998-02-08T00:00:00Z
review text: Paracompact \(p\)-spaces can be defined as topological spaces that are preimages of metric spaces under perfect mappings. The author obtains the following Theorem 2. A paracompact \(p\)-space \(X\) is metrizable if and only if there exists a continuous function \(\varphi:X^3\smallsetminus \Delta\to[-1,1]\) (where \(\Delta\) is the diagonal), satisfying the condition \(\varphi(x,x,y)\neq \varphi(x,y,y)\) for all \(x,y\in X\), \(x\neq y\). Theorem 2 yields the Corollary. For a paracompact \(p\)-space \(X\) the following conditions are equivalent: (1) the space \(X\) is metrizable; (2) \(X^2\smallsetminus \Delta\) admits a \(\sigma\)-locally finite (in \(X^2\smallsetminus \Delta)\) functionally open (in \(X^2\)) covering.
Mathematics Subject Classification ID: 54E18
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 1028479
zbMATH Keywords: paracompact \(p\)-space
author: E. N. Stepanova
MaRDI profile type: Publication
Recommended article: \(P\)-paracompact and \(P\)-metrizable spaces
Recommended article: Q3753111
Recommended article: Q3719477
Recommended article: Extension of continuous functions and metrizability of paracompact \(p\)- spaces
Recommended article: Q5315969
Recommended article: Strongly paracompact metrizable spaces
Recommended article: Paracompact and metacompact spaces in L-topology
Recommended article: Q3733785
Recommended article: A metrisation theorem for pseudocompact spaces
Recommended article: Q3210515
description: scientific article; zbMATH DE number 1028479