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A Typical Nowhere Differentiable Function

Published online by Cambridge University Press:  20 November 2018

F. S. Cater
F. S. Cater*
Affiliation:
Portland State UniversityPortland, Oregon 97207, U.S.A.
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Abstract

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We construct an explicit continuous function F such that for each point x, every extended real number is a derived number of F at x and F has an infinite left and an infinite right derived number at x.

Keywords

26A2726A15nowhere differentiable functioncontinuous functionDini derivatederived number
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 2 , 01 June 1983 , pp. 149 - 151
Copyright
Copyright © Canadian Mathematical Society 1983

References

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3. Jarnik, V., Uber die differenzierbarkeit stetiger funktionen, Fundamenta Mathematicae 21, pp. 48–58 (1933).Google Scholar