Nonshrinking Open Covers and K.Morita's Duality Conjectures
by
Zoltan Balogh
Miami University, Oxford, OH 45056

The following result will be presented. Theorem 1. For every uncountable cardinal k there is a space X such that (a) the product of X with every metrizable space is normal; (b) X has an increasing omega1-cover with no refinement by fewer than k closed subsets of X. Theorem 1 proves Conjecture 9 in M. E. Rudin's problem book paper as well as the second (and thus all three) of K. Morita's duality conjectures.

Date received: February 27, 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 Mathematical Conference Abstracts. Document # cady-67.