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 ...

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 ...

These notes are prepared by Subject Experts of Mathematics including all important topics related to chapter Continuity and Differentiability like continuous functions, sum, difference, product ...

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; ...