Continuous function characterizations of stratifiable spaces
type: Item
instance of: scholarly article
title: Continuous function characterizations of stratifiable spaces
zbMATH Open document ID: 1012.54022
DOI: 10.1023/A:1013839121962
author: Yanyan Li
published in: Acta Mathematica Hungarica
publication date: 2003-05-18T00:00:00Z
review text: Summay: The insertion of a continuous function between pairs of semi-continuous functions in a monotone manner is investigated. In particular, it is established that a topological space is stratifiable if and only if for every pair of semi-continuous functions \(\langle g,h\rangle\), \(g\) upper semi-continuous, \(h\) lower semi-continuous, and \(g\leq h\) (i.e., \(g(x)\leq h(x)\) for each \(x\)) there exists a continuous function \(\phi(\langle g,h\rangle)\) such that \(g\leq \phi(\langle g,h\rangle)\leq h\) and for each \(x\) for which \(g(x)<h(x)\) then \(g(x)<\phi(\langle g,h\rangle)(x)<h(x)\) and if \(\langle g_1,h_1\rangle\) is any other pair of semi-continuous functions with the same properties as \(g\) and \(h\) respectively and \(g\leq g_1\) and \(h\leq h_1\), then \(\phi(\langle g,h\rangle)\leq \phi(\langle g_1,h_1\rangle)\).
Mathematics Subject Classification ID: 54C30
Mathematics Subject Classification ID: 54D15
zbMATH DE Number: 1911994
zbMATH Keywords: monotone insertion property
zbMATH Keywords: stratifiable space
zbMATH Keywords: semi-stratifiable space
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1911994