关于实函数的Dini导数

Pub Date : 2023-01-01 DOI:10.5486/pmd.2023.9221

A. Fonda, Giuliano Klun, Andrea Sfecci

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引用次数: 0

摘要

对于一个连续函数f，由左下导数严格小于右上导数的点组成的集合Vf是完全不连通的。除了连续性外，还提出了其他假设以保持这一性质。另一方面，我们构造一个函数f，它的集合Vf重合于整个定义域，而f在一个可能有无穷多个聚类点的无限集合上是连续的。提出了一些开放性问题。

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On Dini derivatives of real functions

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.

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