The Baire classification of strongly separately continuous functions on $\ell_\infty$

TL;DR

This paper constructs strongly separately continuous functions on __ that precisely belong to specific Baire classes, revealing detailed classification within functional analysis.

Contribution

It demonstrates the existence of strongly separately continuous functions on __ with exact Baire class membership, extending understanding of their classification.

Findings

Existence of functions in each Baire class on __

Functions can be constructed to belong exactly to a given Baire class

Clarifies the relationship between strong separate continuity and Baire classification.

Abstract

We prove that for any $\alpha\in[0,\omega_1)$ there exists a strongly separately continuous function $f:\ell_\infty\to [0,1]$ such that $f$ belongs to the $(\alpha+1)$'th /$(\alpha+2)$'th/ Baire class and does not belong to the $\alpha$'th Baire class if $\alpha$ is finite /infinite/.