International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 7, Pages 381-388
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.
Let be the ideal of functions with pseudocompact
support and let be the set of all points in having compact neighborhoods. We show that
is pure if and only if is a round subset of , is a projective -module if and
only if is pure and is paracompact. We also show that if
pure, then for each the ideal is a projective (flat) -module if and only if is basically disconnected (-space).