The Baire product theorem for separately open sets and separate continuity
by
David Gauld
The University of Auckland
Coauthors: Sina Greenwood (The University of Auckland), Zbigniew Piotrowski (Youngstown State University)

Our main result generalises the Baire Category Theorem as follows:
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 countable sequence of separately semi-closed subsets of the product \prod_i=1^k X_i. Let O be a non-empty open subset of \prod_i=1^k X_i such that O is contained in the union of the sets C_n. Then there is some m such that O meets the interior of C_m.

Applications of this result will be discussed, including the size of the set of points of continuity of a separately continuous function X×Y --> Z.

Date received: June 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 # caeu-31.