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International Journal of Mathematics and Mathematical Sciences
Volume 29, Issue 7, Pages 381-388
http://dx.doi.org/10.1155/S0161171202011067

Purity of the ideal of continuous functions with pseudocompact support

Department of Mathematics, University of Petra, Amman 961343, Jordan

Received 7 November 2000; Revised 29 March 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let CΨ(X) be the ideal of functions with pseudocompact support and let kX be the set of all points in υX having compact neighborhoods. We show that CΨ(X) is pure if and only if βXkX is a round subset of βX, CΨ(X) is a projective C(X)-module if and only if CΨ(X) is pure and kX is paracompact. We also show that if CΨ(X) is pure, then for each fCΨ(X) the ideal (f) is a projective (flat) C(X)-module if and only if kX is basically disconnected (F-space).