The noncommutative topology of one-dimensional spaces
type: Item
instance of: scholarly article
title: The noncommutative topology of one-dimensional spaces
zbMATH Open document ID: 0638.46039
author: Terry A. Loring
published in: Pacific Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: If \(X\) and \(Y\) are compact topological spaces, the unital star-homomorphisms from \(C(X)\) to \(C(Y)\) satisfy certain homotopy properties when X is an absolute neighborhood retract. We show that two of these properties still hold when \(C(Y)\) is replaced by a ``noncommutative space'', i.e. an arbitrary unital \(C^ *\)-algebra, but only under the additional assumption that \(X\) is one-dimensional. Specifally, we show that \(C(X)\) is semiprojective and that two unital star-homomorphisms from \(C(X)\) to a \(C^ *\)-algebra A are homotopic whenever they are close.
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46M40
Mathematics Subject Classification ID: 46L80
Mathematics Subject Classification ID: 47C15
zbMATH DE Number: 4040586
zbMATH Keywords: homotopy
zbMATH Keywords: neighborhood retract
zbMATH Keywords: noncommutative space
zbMATH Keywords: unital \(C^*\)-algebra
zbMATH Keywords: semiprojective
zbMATH Keywords: noncommutative shape theory
zbMATH Keywords: inductive limits
MaRDI profile type: Publication
full work available at URL: pjm.1989.136.145
OpenAlex ID: W2022068659
DOI: 10.2140/PJM.1989.136.145
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description: scientific article; zbMATH DE number 4040586