On strongly separately continuous functions on sequence spaces

TL;DR

This paper investigates the properties of strongly separately continuous functions on sequence spaces, characterizes their determining sets, and explores their Baire class distinctions and discontinuity sets.

Contribution

It provides a characterization of determining sets, constructs functions with specific Baire class properties, and shows that open sets are discontinuity sets for these functions.

Findings

Characterization of determining sets for strongly separately continuous functions

Existence of functions in higher Baire classes that are strongly separately continuous

Any open set in _p can be the discontinuity set of such a function

Abstract

We study strongly separately continuous real-valued function defined on the Banach spaces $\ell_p$. Determining sets for the class of strongly separately continuous functions on $\ell_p$ are characterized. We prove that for every $1\le \alpha<\omega_1$ there exists a strongly separately continuous function which belongs the $(\alpha+1)$'th Baire class and does not belong to the $\alpha$'th Baire class on $\ell_p$. We show that any open set in $\ell_p$ is the set of discontinuities of a strongly separately continuous real-valued function.