The Baire category theorem for separately open sets.
by
David Gauld
The University of Auckland
Coauthors: Sina Greenwood, Zbigniew Piotrowski

After a discussion of the following theorem some applications will be presented. Let X₁, ... , X_k be a finite collection of topological spaces so that X₁ is Baire, and when k > 1 each X_i except possibly X_k has a countable pseudo-base and each X_i except possibly X₁ is quasi-regular and strongly countably complete. Suppose that <C_n > is a sequence of separately closed subsets of the product \prod_i=1^k X_i. Let O subset \prod_i=1^k X_i be a non-empty open set such that O subset \cup _n=1^\infty C_n. Then there is an integer m such that O meets the interior of C_m.

Date received: September 19, 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 # caek-16.