Separately continuous functions on products and its dependence on $\mathrm{\aleph }$ coordinates

It is investigated necessary and sufficient conditions on topological spaces $X=\prod _{s\in S}{X}_s$ and $Y=\prod _{t\in T}{Y}_t$ for the dependence of every separately continuous functions $f:X\times Y\to \mathbb{R}$ on at most $\mathrm{\aleph }$ coordinates with respect to the first or the second variable.