Relating S-derivates to associated sets (Q1824050)

Let \(\Gamma\) be a space of real functions f: [0,1]\(\to R\) that is complete under the sup norm and have an associated set characterization. The authors find a simple system of sets S [in the sense of \textit{B. S. Thomson}, Real Anal. Exch. 8(1982-83), 278-442 (1983; Zbl 0525.26003)] so that the typical function in \(\Gamma\) has both \(\pm \infty\) as S- derivates at every point in the domain. Some new results for Zahorski's classes \({\mathcal M}_ i\), \(i=1,...,5\), are reached.