学术动态

#RAFS^†Session 14

Time：Apr. 16, 2021, 10:00--12:00

Location：434 Qi Xiang Building, Chang'an Campus

Speaker：Mr. Li, Yulong (Class of 2022)

Title：Everywhere continuous nowhere differentiable functions, revisited

Abstract：We discussed last year in this seminar (#MATS Session 3) pathological functions which are everywhere continuous nowhere differentiable. In particular, we presented three kinds ofexplicitexamples with this property: the classical Weierstrass function (1872), Takagi function (1903) & van der Waerden function (1930), and Swift function (1961). In this talk, we will be using the category method on which an existence proof is based. We will show that, in the sense of category, almost all continuous functions are nowhere differentiable; in fact, the set of all continuous functions that have a finite one-sided derivative somewhere is of first category.

† Real Analysis Friday Seminars. Contactshuangshen@nwpu.edu.cnfor any inquiry. For a history of this seminar, please visithttps://teacher.nwpu.edu.cn/2017010194.