Separately continuous functions on products of compact sets and their dependence on $\mathfrak{n}$ variables - Maslyuchenko, V. K.; Mykhailyuk, V. V. (Ukrains’kyi Matematychnyi Zhurnal, 1995)
By using the theorem on the density of the topological product and the generalized theorem on the dependence of a continuous function defined on a product of spaces on countably many coordinates, we show that every separately continuous function defined on a product of two spaces representable as products of compact spaces with density $≤ \mathfrak{n}$ depends on n variables. In the case of metrizable compact sets, we obtain a complete description of the sets of discontinuity points for functions of this sort.