International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 7, Pages 381-388
doi: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 Emad A. Abu Osba. 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 βX−kX 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 f∈CΨ(X) the ideal (f) is a projective (flat) C(X)-module if and only if kX is basically disconnected (F′-space).