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

TL;DR

This paper investigates the conditions under which strongly separately continuous functions on product spaces are continuous and characterizes their discontinuity point sets, especially in countable products of finite-dimensional normed spaces.

Contribution

It provides a necessary and sufficient condition for strong separate continuity to imply continuity and characterizes the discontinuity sets in specific product spaces.

Findings

Necessary and sufficient condition for strong separate continuity to imply continuity.

Characterization of discontinuity point sets in countable products of finite-dimensional normed spaces.

Insights into the behavior of strongly separately continuous functions on product spaces.

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.