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Weakly pseudocompact frames
by
Joann Walters-Wayland
21521 Rushford Drive, Lake Forest CA92630
Coauthors: T.Dube
A completely regular space is pseudocompact iff it is Gδ-dense in each of its compactifiactions. An obvious weakening of this is to require that this holds for some, not all, compactifications. Pseudocompactness in frames has been well explored and has an analogous result: a completely regular frame is pseudocompact iff every compactification is coz-codense (a map is coz-codense if the only cozero mapped to the top is the top itself). Consequently, a similar weakening may be observed. We explore these types of frames and give some additional characterizations in terms of strong inclusions, uniformities and cozero bases – these are internal characterizations and are not translated from spatial results.
Date received: July 10, 2008
Copyright © 2008 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 # caxi-49.