Purity of the ideal of continuous functions with pseudocompact support

Emad A. Abu Osba

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 29, 1-8

Abstract:

Let C Ψ ( X ) be the ideal of functions with pseudocompact support and let k X be the set of all points in υ X having compact neighborhoods. We show that C Ψ ( X ) is pure if and only if β X − k X is a round subset of β X , C Ψ ( X ) is a projective C ( X ) -module if and only if C Ψ ( X ) is pure and k X is paracompact. We also show that if C Ψ ( X ) is pure, then for each f ∈ C Ψ ( X ) the ideal ( f ) is a projective (flat) C ( X ) -module if and only if k X is basically disconnected ( F ′ -space).

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:579857

DOI: 10.1155/S0161171202011067

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