Generalized ordered spaces with < \omega-weakly-uniform bases
by
Harold R Bennett
Texas Tech University
Coauthors: David J. Lutzer

A base B for space X is said to be < \omega-weakly-uniform if, given any infinite subset S subset or equal X there is a finite subset F subset S with the property that only a finite number of members of B contain the set F. This property was introduced in a recent paper by Balogh, Davis, Just, Shelah, and Szeptycki. We investigate the role of such bases among generalized ordered spaces. We prove that any generalized ordered space with such a base must be quasi-develoipable (equivalently, must have a \sigma-disjoint base) and that any linearly ordered topological space with such a base must be metrizable. We also give examples to show that these are the sharpest possible results.

Date received: February 3, 2000

Copyright © 2000 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 # cady-31.