In the space of continuous functions of a real variable, the set of nowhere differentiable functions has long been known to be topologically "generic". In this paper it is shown further that in a ...

Provides a rigorous treatment of topics covered in Calculus 1 and 2. Topics include convergent sequences; continuous functions; differentiable functions; Darboux sums, Riemann sums, and integration; ...

Optimal embeddings of Sobolev type spaces into spaces of continuous functions are established. On extending the classical Morrey embedding on the Hölder continuity of functions with weak derivatives ...