Strong paracompactness and multi-selections
type: Item
instance of: scholarly article
title: Strong paracompactness and multi-selections
zbMATH Open document ID: 1192.54007
author: Takamitsu Yamauchi
author: Valentin Gutev
published in: Topology and its Applications
publication date: 2010-05-19T00:00:00Z
review text: The main theorem of this paper shows that a space \(X\) is strongly paracompact if and only if for each complete metric space \((Y,\rho)\) and each lower semi-continuous closed-valued multifunction \(\Phi:X\to Y\), there is a complete ultrametric space \((Z,d)\), an upper semi-continuous multifunction \(\psi:X\to Z\) and a uniformly continuous \(g:Z\to Y\) such that \(g\psi\) is a multi-selection for \(\Phi\) and \(\psi(\psi^{-1}(S))\) is totally \(\varepsilon\)-bounded when \(\varepsilon>0\) and \(S\subset Z\) is totally \(\varepsilon\)-bounded.
reviewed by: David B. Gauld
Mathematics Subject Classification ID: 54C65
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54F45
zbMATH DE Number: 5710132
zbMATH Keywords: strong paracompactness
zbMATH Keywords: set-valued mapping
zbMATH Keywords: lower semi-continuous
zbMATH Keywords: upper semi-continuous
zbMATH Keywords: multi-selection
zbMATH Keywords: tree
zbMATH Keywords: branch
MaRDI profile type: Publication
full work available at URL: j.topol.2009.06.017
OpenAlex ID: W2006572503
cites work: On monotonic generalizations of Moore spaces, Čech complete spaces and p-spaces
cites work: Q5669947
cites work: Selections, Paracompactness and Compactness
cites work: On selections and classes of spaces
cites work: Q4102463
cites work: Non-Archimedean Metrics in Topology
cites work: Q3994935
cites work: Factorizing dimension-like properties of subsets of topological spaces
cites work: Completeness, sections and selections
cites work: Set theory. An introduction to independence proofs. 2nd print
cites work: Continuous selections. I
cites work: Continuous selections. II
cites work: Continuous selections. III
cites work: A theorem on semi-continuous set-valued functions
cites work: Complete spaces and tri-quotient maps
cites work: Characterizations of paracompact-like properties by means of set-valued semi-continuous selections
cites work: Q3879935
cites work: Q3954493
cites work: On some non-Archimedian spaces of Alexandroff and Urysohn
cites work: Q4457275
cites work: Q4117063
cites work: Q5436537
DOI: 10.1016/J.TOPOL.2009.06.017
description: scientific article; zbMATH DE number 5710132