Characterizing global properties in inverse limits
type: Item
instance of: scholarly article
title: Characterizing global properties in inverse limits
zbMATH Open document ID: 0546.55011
author: Zvonko Čerin
published in: Pacific Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: The inverse limit X of an inverse sequence (inverse system indexed by the positive integers) \(\{X_ i,P_{i+1,i}\}\) of compact metric spaces, may fail to be locally connected (n-LC for some or all n) even when the bonding maps are sufficiently nice and each \(X_ i\) is a manifold. For instance, consider the 2-adic solenoid as the inverse limit of an inverse sequence where \(X_ i\) is the circle and the bonding map is the 2-fold covering map. The author gives several necessary and sufficient conditions on X which suitably insure that X is, for instance, an absolute neighborhood retract, \(LC^ n\) (locally connected) up to dimension n, or n-dimensional, the results and related techniques are motivated by shape theory. The paper contains many other results which are too technical to be included in this brief review.
Mathematics Subject Classification ID: 55P55
Mathematics Subject Classification ID: 55M10
Mathematics Subject Classification ID: 54B35
Mathematics Subject Classification ID: 54C56
Mathematics Subject Classification ID: 54C55
Mathematics Subject Classification ID: 57N25
zbMATH DE Number: 3870212
zbMATH Keywords: inverse limit
zbMATH Keywords: inverse sequence
zbMATH Keywords: compact metric spaces
zbMATH Keywords: manifold
zbMATH Keywords: absolute neighborhood retract
zbMATH Keywords: up to dimension n
zbMATH Keywords: n-dimensional
zbMATH Keywords: shape theory
reviewed by: Sukhjit Singh
MaRDI profile type: Publication
full work available at URL: pjm.1984.112.49
OpenAlex ID: W2030376273
DOI: 10.2140/PJM.1984.112.49
description: scientific article; zbMATH DE number 3870212