Nonlocal uniform algebras on three-manifolds
type: Item
instance of: scholarly article
title: Nonlocal uniform algebras on three-manifolds
zbMATH Open document ID: 1262.46033
author: Alexander J. Izzo
published in: Pacific Journal of Mathematics
publication date: 2012-11-21T00:00:00Z
full work available at URL: p05.xhtml
review text: Let \(A\) be a uniform algebra on a compact Hausdorff space \(X\). A function \(f\in C(X)\) is said to belong locally on \(X\) to \(A\) if, for each point \(x\in X\), there are a neighborhood \(N\) of \(x\) and a function \(g\in A\) coinciding with \(f\) on \(N\). The algebra \(A\) is said to be local on \(X\) if every function that belongs locally on \(X\) to \(A\) is in \(A\). The algebra \(A\) is local if it is local on its maximal ideal space. The note under review contains a theorem which says that, on every compact \(C^\infty\)-manifold \(M\) of dimension greater than or equal to three, there exists a nonlocal uniform algebra with maximal ideal space \(M\) generated by \(C^\infty\)-smooth functions. In the proof of the result, the author uses two interesting (technical) lemmas.
reviewed by: Janusz Godula
Mathematics Subject Classification ID: 46J10
Mathematics Subject Classification ID: 46J15
Mathematics Subject Classification ID: 30H50
Mathematics Subject Classification ID: 30J15
zbMATH DE Number: 6109305
zbMATH Keywords: nonlocal uniform algebra
zbMATH Keywords: three-manifold
zbMATH Keywords: maximal ideal space
MaRDI profile type: Publication
OpenAlex ID: W2158579128
DOI: 10.2140/PJM.2012.259.109
description: scientific article; zbMATH DE number 6109305