Finite graphs that are inverse limits with a set valued function on \([0,1]\).
type: Item
instance of: scholarly article
title: Finite graphs that are inverse limits with a set valued function on \([0,1]\).
zbMATH Open document ID: 1236.54017
published in: Topology and its Applications
publication date: 2011-07-07T00:00:00Z
review text: An arc is the inverse limit of the diagonal in \([0,1] \times [0,1]\). This presents the only known example of a closed subset of \([0,1] \times [0,1]\) whose generalized inverse limit is a finite graph. \textit{A. Illanes} has shown that a simple closed curve is not the generalized inverse limit of a closed subset of \([0,1] \times [0,1]\) [Proc. Am. Math. 139, No. 8, 2987--2993 (2011; Zbl 1232.54030)]. In the paper under review, Nall shows that the only finite graphs that can be obtained as inverse limits with a simple surjective upper semi-continuous bonding function from \([0,1]\) to the nonempty closed subsets of \([0,1]\) are an arc or a simple triod. However, it is not known if there is such a simple triod.
reviewed by: K. T. Hallenbeck
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54D80
Mathematics Subject Classification ID: 54F50
zbMATH DE Number: 5918212
zbMATH Keywords: inverse limit
zbMATH Keywords: generalized inverse limit
zbMATH Keywords: set-valued functions
author: Van Nall
MaRDI profile type: Publication
full work available at URL: j.topol.2011.04.011
OpenAlex ID: W1992841291
cites work: A circle is not the generalized inverse limit of a subset of [0,1]²
cites work: Q3562037
cites work: Q5479987
cites work: Connected generalized inverse limits
cites work: Inverse limits with subsets of \([0,1]\times[0,1]\)
cites work: Q3115801
cites work: Q3417879
DOI: 10.1016/J.TOPOL.2011.04.011
description: scientific article; zbMATH DE number 5918212