Variants of Compactness in Pointfree Topology
by
Bernhard Banaschewski
Department of Mathematics & Statistics, McMaster University, Hamilton, Ontario, Canada

Motivated by the fact that the compactness of a space may be expressed in terms of the convergence of certain filters, we study conditions of this type in pointfree topology, replacing classical (2-valued) filters by their general counterparts, the bounded meet-semilattice homomorphisms into arbitrary frames (instead of 2) and using the natural extension of the notion of convergence to this setting. In particular, we obtain some coproduct and coreflection results and establish an interesting connection with the Axiom of Countable Choice. This is joint work with S.S. Hong.

Date received: April 14, 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 # caeq-03.