On the differences of Darboux upper semicontinuous functions (Q1912729)

The author deals with real functions of a real variable. In 1921, W. Sierpiński showed that the class \(\widehat B_1\) of all differences of two upper semicontinuous functions is a proper subset of the class of all Baire one functions. It is shown, in this paper, that the class of all Darboux functions in \(\widehat B_1\) is the class of all functions which can be written as the difference of two Darboux upper semicontinuous functions. This gives an answer on a problem raised by \textit{J. G. Ceder} and \textit{T. L. Pearson} [Real Anal. Exch. 9, 179-194 (1984; Zbl 0579.26002)].