On the sums of unilaterally approximately continuous and approximate jump functions.

Abstract

In paper \cite{Mar} it is proved that every jump function \(f:{\mathbb R} \to {\mathbb R}\) is the sum of two unilaterally continuous jump functions. In this article we prove that the analogous result is not true for the density topology. Moreover we show some necessary and sufficient conditions ensuring that an approximate jump function is the sum of two unilaterally approximately continuous and approximate jump functions.