Dependence of separately continuous functions on n coordinates on products of compact sets

We investigate the problem of the dependence of separately continuous functions on n coordinates on products of spaces each of which is a topological product. In the case where X and Y are products of completely regular countably compact spaces, we establish necessary and sufficient conditions for such a dependence. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 6, pp. 822–829, June, 1998.