Abstract:
For a continuous function f, the set Vf made of those points
where the lower left derivative is strictly less than the upper right derivative is totally disconnected. Besides continuity, alternative assumptions
are proposed so to preserve this property. On the other hand, we construct a function f whose set Vf coincides with the entire domain, and
nevertheless f is continuous on an infinite set, possibly having infinitely
many cluster points. Some open problems are proposed.
