On essential derived numbers of typical continuous functions. (English) Zbl 0793.26009
In this paper the author proves that, in the space of all continuous functions (with the metric of uniform convergence), the set formed by functions such that, for each \(x\in (0,1)\), there exists \(y\in\overline R\) which is a symmetrical essential derived number of \(f\) at \(x\), is residual.
Reviewer: R.Pawlak (Łódź)
MSC:
26A24 | Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems |
28A05 | Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets |