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, for any given totally disconnected closed set A, we construct a function f whose set Vf coincides with the entire domain, and f is continuous on A.
On Dini derivatives of real functions
Fonda, Alessandro;Klun, Giuliano;Sfecci, Andrea
2023-01-01
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, for any given totally disconnected closed set A, we construct a function f whose set Vf coincides with the entire domain, and f is continuous on A.File in questo prodotto:
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