When |C(X ×Y)| = |C(X)| |C(Y)| ?
by
Melvin Henriksen
Harvey Mudd College, Claremont CA

This report and that of R.G. Woods are complementary and they report on the results of a group including also O. Alas, W. Comfort, S. Garcia-Ferrira, and R.G. Wilson. As usual, C(X) denotes the set of real-valued functions on a Tychonoff space X, and |S| is the cardinal number of the set S. The condition of the title is satisfied if X is separable, or if X×Y is pseudocompact, weakly Lindelöf, or metrizable. (As will be shown by Woods, it is not enough to assume that each of X, Y is countably compact or each is Lindelöf.) Many other affirmative results will be stated; e.g., it is enough to assume that if X has a dense C^*-embedded metrizable subspace, and |C(Y)| is an infinite power of 2 or |C(Y)| <= |C(X)|, then the condition of the title holds.

Date received: June 29, 1997

Copyright © 1997 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 # caao-44.