The Pointwise Limit of Separately Continuous Functions

Abstract

The motivation for this paper is due to a question from Z. Piotrowski on whether or not the \textquotedblleft salt-and-pepper\textquotedblright\ function in the plane was the pointwise limit of separately continuous functions. In this paper we answer that question and then go on to investigate the sets $D$ in the plane such that $\chi _{D}$ is the pointwise limit of separately continuous functions. We also look at all pointwise limits of separately continuous functions and their place in the space of Baire Class 2 functions.