Differentiability, Continuity, and Existence of Limits
Date of Graduation
Master of Science in Mathematics
In this thesis, we first demonstrate in various aspects the existence of everywhere continuous nowhere differentiable functions. We then address the question: could there exist a function defined on R that has a limit at each point of R, but fails to be continuous at any point? We show that the answer to this question is "No", and we establish the stronger result that if a function defined on the interval [a,b] has a limit at each point of a dense subset of [a,b], then the set of points where the function is continuous is dense, uncountable, and has the same cardinality as R.
© Julie Ann Millett
Millett, Julie Ann, "Differentiability, Continuity, and Existence of Limits" (1994). MSU Graduate Theses. 860.