On the Sums of Two Quasi-Continuous Functions with Closed Graphs

Abstract

In 2000 J.Borsík, J. Doboš, and M. Repický characterized sums of quasi-continuous functions with closed graphs. More precisely, they showed that such a sum must be Baire one star, and proved that each Baire one star function defined on a separable metric space which is Baire in the strong sense is the sum of three quasi-continuous functions with closed graphs. They showed also that not every Baire one star function defined on $\mathbb{R}$ is the sum of two quasi-continuous functions with closed graphs, and asked for characterization of such sums. The goal of this article is to present the required characterization.