Differentiability, Continuity, and Existence of Limits

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.

Name thesis:degree_name

Master of Science in Mathematics

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Mathematics

Year

1994

Author dc:creator

• Millett, Julie Ann

Contributors dc:contributor

• Xingping Sun

• Mathematics

Statement dc:rights

• © Julie Ann Millett

Repository record dc:identifier

https://bearworks.missouristate.edu/theses/860

OAI identifier oai:identifier

oai:bearworks.missouristate.edu:theses-1861