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On open ultrafilters and maximal points
by
Nathan Carlson
University of Arizona
Coauthors: Jack R. Porter
We study open ultrafilters in the setting of regular spaces. In 1981, E. van Douwen showed that if X is a non-feebly compact Tychonoff space with a countable -base, then X has a remote point. We develop a related result for the class of regular spaces which shows that in a non-feebly compact regular space with a countable -base, there exists a free open ultrafilter on X that is also a regular filter. We also extend results of Smirnov and Skljarenko by showing maximal regular open filters are disjoint-prime. Finally, we show that a maximal point in a T_2 space cannot have a neighborhood base of feebly compact neighborhoods. One corollary is that no locally countably compact T_2 topology is a lower topology in the partial order of T_2 topologies. This extends a result of Alas and Wilson.
Date received: February 9, 2009
Copyright © 2009 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 # caxy-47.