On the differences of lower semicontinuous functions (Q1704494)

The so-called \textit{Sierpiński class one} consists of functions of the form \(f-g\), where \(f\) and \(g\) are lower semicontinuous functions. A bounded almost everywhere continuous Darboux function from this class is constructed which allows \(f\), \(g\) in the above representation to be neither bounded nor a.e.\ continuous. The construction provides a negative answer to some problems posed by \textit{A. Maliszewski} [Real Anal. Exch. 21, No. 1, 258--263 (1996; Zbl 0853.26004)].