Purity of the ideal of continuous functions with pseudocompact support
type: Item
instance of: scholarly article
title: Purity of the ideal of continuous functions with pseudocompact support
zbMATH Open document ID: 0993.54016
DOI: 10.1155/S0161171202011067
author: Emad A. Abu Osba
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2002-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/49391
full work available at URL: S0161171202011067.html
review text: Summary: Let \(C_\Psi(X)\) be the ideal of functions with pseudocompact support and let \(kX\) be the set of all points in \(\upsilon X\) having compact neighborhoods. We show that \(C_\Psi(X)\) is pure if and only if \(\beta X-kX\) is a round subset of \(\beta X, C_\Psi(X)\) is a projective \(C(X)\)-module if and only if \(C_\Psi(X)\) is pure and \(kX\) is paracompact. We also show that if \(C_\Psi(X)\) is pure, then for each \(f \in C_\Psi(X)\) the ideal \((f)\) is a projective (flat) \(C(X)\)-module if and only if \(kX\) is basically disconnected (\(F'\)-space).
Mathematics Subject Classification ID: 54C40
Mathematics Subject Classification ID: 13C11
Mathematics Subject Classification ID: 54C30
zbMATH DE Number: 1780356
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1780356