A characterization of the discontinuity point set of strongly separately continuous functions on products

Abstract: We study properties of strongly separately continuous mappings defined on subsets of products of topological spaces equipped with the topology of pointwise convergence. In particular, we give a necessary and sufficient condition for a strongly separately continuous mapping to be continuous on a product of an arbitrary family of topological spaces. Moreover, we charac-terize the discontinuity point set of strongly separately continuous function defined on a subset of countable product of finite-dimensional normed spaces.