The Closed Continuous \epsilon-Chain Axiom
by
Paul Szeptycki
Ohio University

The Closed Continuous \epsilon-Chain Axiom (CECA) was recently introduced in the paper ``Strongly almost disjoint sets and weakly uniform bases'' by Balogh, Davis, Just, Shelah and Szeptycki. CECA is equivalent to GCH + known weakenings of \square_\lambda for all singular limit cardinals \lambda. However, CECA has a decidedly different flavor than \square_\lambda. Some consequences of CECA include

1. Generalizations of the statement that every strongly almost disjoint family is essentially disjoint.
2. Every first countable space with a weakly uniform base has a point-countable base.
3. For every Hausdorff topological space X, X \not --> (top2^\omega)¹₂.

Date received: April 11, 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 # cadv-12.