Connected generalized inverse limits
type: Item
instance of: scholarly article
title: Connected generalized inverse limits
zbMATH Open document ID: 1234.54022
author: Sina Greenwood
author: Judy Kennedy
published in: Topology and its Applications
publication date: 2011-12-06T00:00:00Z
review text: For \(i>0\), let \(f_i:I_i\to 2^{I_{i-1}}\) be a surjective upper semicontinuous function whose graph is connected, where the \(I_i\) are closed intervals. The authors introduce a technical condition, called a C-sequence, on the sequence \(\{f_i\}\), which implies that the inverse limit of this sequence is not connected. More precisely, they prove that the sequence \(\{f_i\}\) has a C-sequence iff there exist integers \(n\geq0\) and \(m>n+1\) such that, for \(n\leq i\leq m\), there exist an open interval \(U_i\) and a closed interval \(A_i\) with \(A_i\subset U_i\subset I_i\), \(U_i\neq I_i\) and \(\varprojlim(I_i,f_i)\cap(\prod_{0\leq i<n}I_i \times \prod_{n\leq i\leq m}U_i\times\prod_{i=m+1}^\infty I_i)=\varprojlim(I_i,f_i)\cap(\prod_{0\leq i<n}I_i\times\prod_{n\leq i\leq m}A_i \times\prod_{i=m+1}^\infty I_i)\neq\emptyset\).
reviewed by: Robert Cauty
Mathematics Subject Classification ID: 54B99
zbMATH DE Number: 5986541
zbMATH Keywords: generalized inverse limit
MaRDI profile type: Publication
full work available at URL: j.topol.2011.07.019
OpenAlex ID: W2079895750
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DOI: 10.1016/J.TOPOL.2011.07.019
description: scientific article; zbMATH DE number 5986541