Mel and the Question "When is |C(X×Y)|=|C(X)|·|C(Y)|?"
by
W. Wistar Comfort
Wesleyan University, Middletown, CT

Mel knows a lot about continuous functions. He knows a lot about the product topology. He knows a lot about infinite cardinal numbers. That makes you wonder: How come it took Mel 75 years to ask the question:

When Is |C(X×Y)|=|C(X)|·|C(Y)|?

Mel posed that question at a public forum, and several of us jumped on the bandwagon. With Mel leading the way as principal researcher, inspirational leader, cheerleader and scribe, a paper finally emerged:

O. T. Alas, W. W. Comfort, S. Garcia-Ferreira, M. Henriksen, R. G. Wilson and R. G. Woods, When Is |C(X×Y)|=|C(X)|·|C(Y)|?, Houston J. Math. 26 (2000), 83-115.

None of those authors, Mel included, knows the full answer to the question. We do know that for some pairs (X, Y) the equality holds, and for others it fails. In this talk I aspire to cite some of the principal results of that paper, with examples of pairs of each kind, and I hope also to have time to state what are in my opinion the two or three most compelling unsolved problems.

Date received: February 22, 2002