Product invariance of C-spaces and Cs-spaces

Determine whether the category-theoretic product of two C-spaces is again a C-space and, analogously, whether the product of two Cs-spaces is again a Cs-space.

Background

The paper shows that product invariance fails for several related classes (e.g., C(ℱ), C(M), and C(Mc)), and products of Br-spaces can also fail to be Br. Despite these negative results, the general situation for C-spaces and Cs-spaces (defined with respect to all Hausdorff source spaces and separating maps, respectively) remains unsettled.

The authors state that the product invariance problem for C- and Cs-spaces is open, with an expected negative outcome, but no definitive proof is currently known.