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17th "Summer" Conference on Topology and Applications
July 1-4, 2002
University of Auckland
Auckland, New Zealand

Organizers
David Gauld (University of Auckland), Sina Greenwood (University of Auckland), David McIntyre (University of Auckland), Warren Moors (Waikato University), Sidney Morris (University of South Australia), Vladimir Pestov (Victoria University Wellington), Ivan Reilly (University of Auckland), Des Robbie (University of Melbourne)

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When all prime z-ideals of C(X) are either minimal or maximal
by
Grant Woods
University of Manitoba
Coauthors: Melvin Henriksen (Harvey Mudd College), Jorge Martinez (University of Florida)

All hypothesized spaces are assumed to be Tychonoff. A space X is called a P-space if all its zero-sets are open. It is well-known that X is a P-space iff all the prime z-ideals of C(X) are maximal.

Definition: A space X is called quasi-P if the prime z-ideals of C(X) are either minimal or maximal.

We characterize those quasi-P spaces that are locally compact and normal, and present examples showing that the characterization fails if either local compactness or normality is dropped. One example is a countable nodec quasi-P space without isolated points. We consider conditions under which continuous images of quasi-P spaces are quasi-P.

Date received: May 31, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cait-29.