Normality in Products with a Countably Tight Factor
by
Peter Nyikos
University of South Carolina

Some classes of normal spaces have nice extensions which make it possible to transfer information from the extension to the space when dealing with products where the other factor has countable tightness or some similar property.

Call a filterbase B on X strongly \omega-SC if for each open cover U of X, there is an open set S meeting each member of B and such that every countable subset of S is covered by finitely many members of U. Then we have:

Theorem. If X is a normal space and X* is the subspace of \betaX obtained by adding points to which a strongly \omega-SC filterbase on X converges, and Y countably tight, then disjoint closed sets in X ×Y have disjoint closures in X* ×Y.

Corollaries include S. Purisch's recent result that the product of a suborderable space and a countable regular space is normal, and Kombarov's 1972 result that an \omega-bounded normal space has a normal product with any paracompact space of countable tightness.

Date received: April 12, 1996

Copyright © 1996 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 # caae-59.