Spaces X such that the space of minimal prime ideals of C(X) is compact- continued
by
Melvin Henriksen
Harvey Mudd College

Spaces with this property have been characterized some time ago as those for which every cozerset C has a cozero complement C' disjoint from it such that the union of C and C' is dense. Inspired by a preprint of R. Levy and J. Shapiro, the study continues on what kinds of open or dense subspaces of cozero complemented spaces are cozero complemented, and of the relationship between two spaces having this property and their product having it. Mappings that preserve this property directly or inversely are also examined. Many partial answers to some natural questions raised by Levy and Shapiro are given, but many remain open. What will be presented is part of joint research with R.G. Woods, and many of our results depend on theorems proved by R. Blair, W.W. Comfort, A. Hager, and J. Martinez.

Date received: May 11, 2003