Paracompact box products equals finite powers Hurewicz
by
Scott Williams
SUNY at Buffalo

We establish

Theorem. The box product of countably many s-compact metric or s-compact separable linear ordered spaces is paracompact. (Assume b = d or d = c.)

This improves Lawrence's theorem [1988] with all factors the rationals and Winger's theorem [1994] with all factors sigma-compact zero-dimensional metric spaces. We use

Lemma. Suppose that X is a separable space which is either metric or linear ordered. Then ∏^N X is paracompact if and only if all finite powers of X are Hurewicz. (Assume b = d or d = c.)

Date received: January 14, 2008

Copyright © 2008 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 # cawk-17.