A theorem of Nepomnyashchii on continuous subset-selections
type: Item
instance of: scholarly article
title: A theorem of Nepomnyashchii on continuous subset-selections
zbMATH Open document ID: 1071.54008
published in: Topology and its Applications
publication date: 2004-11-23T00:00:00Z
review text: Let \(X\) be a paracompact space, \(Y\) a completely metrizable one, and \(F: X\to Y\) a lower-semicontinuous multifunction with closed and equi-\(\text{LC}^0\) values. Let \(G: X\to Y\) be any upper-semicontinuous relation with compact (possibly empty) values such that \(G(x)\subset F(x)\), \(x\in X\). The following sandwich theorem is proved: if every \(F(x)\) is connected then there exists a continuous multifunction \(H: X\to Y\) with compact and connected values such that \(G(x)\subset H(x)\subset F(x)\), \(x\in X\). When \(G(x)= \emptyset\), \(x\in X\) this reduces to a multiselection theorem of Nepomnyashchii, although the proof is different. Four examples illustrating the essentiality of the assumptions are provided.
Mathematics Subject Classification ID: 54C65
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 2117956
zbMATH Keywords: multifunction
zbMATH Keywords: multiselection
zbMATH Keywords: equi-\(\text{LC}^0\)
zbMATH Keywords: sandwich theorem
author: E. Michael
reviewed by: Włodzimierz Ślęzak
MaRDI profile type: Publication
full work available at URL: j.topol.2004.02.004
OpenAlex ID: W2090759963
cites work: Representing spaces as images of zero-dimensional spaces
cites work: Q3868444
cites work: Q3994935
cites work: Extensions by means of expansions and selections
cites work: Hyperspaces of a Continuum
cites work: Topologies on Spaces of Subsets
cites work: Continuous selections. II
cites work: On many-valued continuous selections
cites work: Continuous multivalued selections of lower semicontinuous mappings
cites work: Q3027880
cites work: Q3409153
DOI: 10.1016/J.TOPOL.2004.02.004
description: scientific article; zbMATH DE number 2117956