Insertion theorems for maps to Banach lattices
type: Item
instance of: scholarly article
title: Insertion theorems for maps to Banach lattices
zbMATH Open document ID: 1203.54029
author: Kaori Yamazaki
published in: Topology and its Applications
publication date: 2010-06-22T00:00:00Z
review text: Semicontinuous maps from topological spaces into vector lattices are investigated. For a topological space \(X\) and an ordered topological vector space \(Y\) we say that \((X,Y)\) has the insertion property if for every upper semicontinuous map \(g: X\to Y\) and every lower semicontinuous map \(h: X\to Y\) with \(g\leq h\), there exists a continuous map \(f: X\to Y\) such that \(g\leq f\leq h\). In the paper there are several insertion theorems for maps from a topological space to Banach lattices. Similarly, for a topological space \(X\) and an ordered topological vector space \(Y\), we say that \((X,Y)\) has the one-side insertion property if for every upper semicontinuous map \(g: X\to Y\) there exists a continuous map \(f: X\to Y\) such that \(g\leq f\) or for every lower-continuous map \(h: X\to Y\) there exists a continuous map \(f: X\to Y\) such that \(f\leq h\). In the paper there are also results on one-side insertion property for maps from topological space to Banach lattices.
reviewed by: Stefan Czerwik
Mathematics Subject Classification ID: 54H12
zbMATH DE Number: 5724590
zbMATH Keywords: topological vector lattice
zbMATH Keywords: lower(upper) semicontinuous map
zbMATH Keywords: insertion property
zbMATH Keywords: one-side insertion property
MaRDI profile type: Publication
full work available at URL: j.topol.2010.04.009
OpenAlex ID: W2073872741
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DOI: 10.1016/J.TOPOL.2010.04.009
description: scientific article; zbMATH DE number 5724590