Date of Award
4-17-2008
Degree Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics and Statistics
First Advisor
Mihaly Bakonyi - Chair
Second Advisor
Lifeng Ding
Third Advisor
Irme Patyi
Abstract
In this paper we examine continuous functions which on the surface seem to defy well-known mathematical principles. Before describing these functions, we introduce the Baire Category theorem and the Cantor set, which are critical in describing some of the functions and counterexamples. We then describe generic continuous functions, which are nowhere differentiable and monotone on no interval, and we include an example of such a function. We then construct a more conceptually challenging function, one which is everywhere differentiable but monotone on no interval. We also examine the Cantor function, a nonconstant continuous function with a zero derivative almost everywhere. The final section deals with products of derivatives.
DOI
https://doi.org/10.57709/1059700
Recommended Citation
Woolley, Douglas Albert, "Generic Continuous Functions and other Strange Functions in Classical Real Analysis." Thesis, Georgia State University, 2008.
doi: https://doi.org/10.57709/1059700