Approximate inverse systems of compacta and covering dimension
type: Item
instance of: scholarly article
title: Approximate inverse systems of compacta and covering dimension
zbMATH Open document ID: 0631.54006
author: Sibe Mardešić
author: Leonard R. Rubin
published in: Pacific Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.pjm/1102650284
review text: Approximate inverse systems of metric compacta are introduced and studied. The bonding maps in these systems commute only up to certain controlled values. With every such system \(X=(X_ a,\epsilon _ a,p_{aa'},A)\) are associated a limit space X and projection \(p_ a:X\to X_ a\). A compact Hausdorff space X has covering dimension dim \(X\leq n\) if and only if it can be obtained as the limit of an approximate inverse system of compact polyhedra of dimension \(\leq n\). The analogous statement for usual inverse systems is known to be false.
Mathematics Subject Classification ID: 54B35
Mathematics Subject Classification ID: 54F45
Mathematics Subject Classification ID: 54D30
zbMATH DE Number: 4026318
zbMATH Keywords: compact Hausdorff space
zbMATH Keywords: covering dimension
zbMATH Keywords: approximate inverse system of compact polyhedra
zbMATH Keywords: inverse limit
MaRDI profile type: Publication
OpenAlex ID: W1973193518
DOI: 10.2140/PJM.1989.138.129
description: scientific article; zbMATH DE number 4026318