Productivity of properties of topological groups (Q1203835)

A short and clear proof is given of the fact that every continuous mapping of a weakly Lindelöf Malcev subspace of an arbitrary product of Malcev spaces to a space with strong \(G_ \delta\)-diagonal depends on at most countably many coordinates; the corresponding factorization is not necessarily continuous. It is interesting to compare this theorem with an earlier result of the reviewer [Czech. Math. J. 38, 324-341 (1988; Zbl 0664.54006)] on continuous factorization of real-valued functions defined on a Lindelöf (or totally bounded) subgroup of a topological group product proved in an absolutely different way. The author applies the theorem to give another self-contained and direct proof of the Comfort-Ross theorem on the product of pseudocompact topological groups and the reviewer's generalization of it to relatively pseudo-compact subsets of topological groups.