\(C_\infty(X)\) and related ideals
type: Item
instance of: scholarly article
title: \(C_\infty(X)\) and related ideals
zbMATH Open document ID: 1245.54019
published in: Real Analysis Exchange
publication date: 2012-05-10T00:00:00Z
review text: The intersection of all free maximal ideals of \(C^*(X)\) is denoted by \(C_\infty(X)\) and the smallest (possibly improper) \(z\)-ideal containing \(C_\infty(X)\) is denoted by \(C_{l\sigma}(X)\). Spaces for which \(C_{l\sigma}(X)\) is a prime ideal are characterized and it is shown that \(C_\infty(X)\) is a \(z\)-ideal in \(C(X)\) if and only if every zero-set contained in an open, locally compact and \(\sigma\)-compact subset of \(X\) is compact.
reviewed by: Richard G. Wilson
Mathematics Subject Classification ID: 54C40
zbMATH DE Number: 6032472
zbMATH Keywords: zero-set
zbMATH Keywords: \(z\)-ideal
zbMATH Keywords: maximal ideal
zbMATH Keywords: prime ideal
zbMATH Keywords: \(C_\infty(X)\)
zbMATH Keywords: essential ideal
zbMATH Keywords: locally compact space
zbMATH Keywords: \(\sigma\)-compact space
MaRDI profile type: Publication
full work available at URL: realanalexch.36.1.0045
OpenAlex ID: W2051535990
DOI: 10.14321/REALANALEXCH.36.1.0045
author: S. Afrooz
author: Mehrdad Namdari
description: scientific article; zbMATH DE number 6032472