Separately continuous functions on products of compact sets and their dependence on$\mathfrak{n}$ variables

Abstract

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$\mathfrak{n}$ variables. In the case of metrizable compact sets, we obtain a complete description of the sets of discontinuity points for functions of this sort.