Book:Johan Thim/Continuous Nowhere Differentiable Functions
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Johan Thim: Continuous Nowhere Differentiable Functions
Published $2003$, Luleå University of Technology Master's Thesis.
Online copies
hosted by Luleå University of Technology
Contents
- 1 Introduction
- 2 Series and Convergence
- 3 Functions Through the Ages
- 3.1 Bolzano function (≈1830)
- 3.2 Cellérier function (≈1860)
- 3.3 Riemann function (≈1861)
- 3.4 Weierstrass function (1872)
- 3.5 Darboux function (1873)
- 3.6 Peano function (1890)
- 3.7 Takagi (1903) and van der Waerden (1930) functions
- 3.8 Koch "snowflake" curve (1904)
- 3.9 Faber functions (1907, 1908)
- 3.10 Sierpiński curve (1912)
- 3.11 Knopp function (1918)
- 3.12 Petr function (1920)
- 3.13 Shoenberg function (1938)
- 3.14 Orlicz functions (1947)
- 3.15 McCarthy function (1953)
- 3.16 Katsuura function (1991)
- 3.17 Lynch function (1992)
- 3.18 Wen function (2002)
- 4 How "Large" is the Set $\mathcal{ND}[a,b]$
- 4.1 Metric spaces and category
- 4.2 Banach-Mazurkiewicz theorem
- 4.3 Prevalence of $\mathcal{ND}[0,1]$
- Bibliography
- Index
- Index of Names
- Index of Subjects