Sufficient conditions on the Tychonoff spaces X and Y are found that imply that the equation in the title holds. Sufficient conditions on the Tychonoff space X are found that ensure that the equation holds for every Tychonoff space Y . A series of examples (some using rather sophisticated cardinal arithmetic) are given that witness that these results cannot be generalized much.
© 2000 Houston Journal of Mathematics
Alas, O. T., W. W. Comfort, S. Garcia-Ferreira, M. Henriksen, R. G. Wilson, and R. G. Woods. “When is |C(X x Y)| = |C(X)||C(Y)|?” Houston Journal of Mathematics 26.1 (2000): 83–115.