Paths through inverse limits
type: Item
instance of: scholarly article
title: Paths through inverse limits
zbMATH Open document ID: 1223.54023
author: Iztok Banič
author: Matevž Črepnjak
author: Matej Merhar
author: Uroš Milutinović
published in: Topology and its Applications
publication date: 2011-07-07T00:00:00Z
review text: Soit \(X\) un espace métrique compact, et soit \(\prod X=\prod_{i=1}^\infty X_i\), où \(X_i=X\) pour tout \(i\). Si \(f:X\to X\) est une fonction multivoque semi-continue supérieurement (s.c.s.), soit \(\Gamma(f)\subset X\times X\) son graphe, et soit \(K(f)\subset\prod X\) la limite projective de la suite \((X_i,f_i)\) où \(X_i=X\) et \(f_i=f\) pour tout \(i\). Etant donnée une suite \((f_n)\) de fonctions s.c.s. de \(X\) dans \(X\), les auteurs s'intéressent aux relations entre la convergence des graphes \(\Gamma(f_n)\) vers \(\Gamma(f)\) dans \(2^{X\times X}\) et la convergence de \(K(f_n)\) vers \(K(f)\) dans \(2^{\prod X}\). Notant \(\pi_1\) la projection de \(\prod X\) sur \(X_1=X\), ils montrent en particulier que si \(\Gamma(f_n)\) converge vers \(\Gamma(f)\) et si \(f\) est univoque, alors \(K(f_n)\) converge vers \(K(f)\) si, et seulement si, \(\pi_1(K(f_n))\) converge vers \(\pi_1(K(f))\).
reviewed by: Robert Cauty
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54D80
Mathematics Subject Classification ID: 54F65
Mathematics Subject Classification ID: 54B99
zbMATH DE Number: 5918197
zbMATH Keywords: inverse limits
zbMATH Keywords: upper semi-continuous set-valued functions
MaRDI profile type: Publication
full work available at URL: j.topol.2011.03.001
OpenAlex ID: W2008094981
cites work: Q3514356
cites work: Limits of inverse limits
cites work: Q4004856
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cites work: Q4512386
cites work: Q5479987
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cites work: Inverse limits with subsets of \([0,1]\times[0,1]\)
cites work: Q4064159
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DOI: 10.1016/J.TOPOL.2011.03.001
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description: scientific article; zbMATH DE number 5918197