Separately continuous functions of many variables on product of spaces which are products of metrizable multipliers

TL;DR

This paper characterizes the dependence on coordinates and the discontinuity points of functions of multiple variables, each being a product of metrizable spaces, with a focus on separable metrizable factors.

Contribution

It provides necessary and sufficient conditions for coordinate dependence and characterizes discontinuity sets for functions on products of metrizable spaces.

Findings

Conditions for dependence on coordinates are established.

Discontinuity points are characterized for functions on products of separable metrizable spaces.

Results extend understanding of separately continuous functions in product spaces.

Abstract

It is obtained necessary and sufficient conditions of dependence on $\aleph$ coordinates for functions of several variables, each of which is a product of metrizable factors. The set of discontinuity points of such functions is characterized in the case, when each variable is a product of separable metrizable spaces.