Math 131 112816 Uniform Convergence and Differentiation, Nowhere differentiable continuous function

When can one commute limit and differentiation? (continued from previous lecture). Construction of a continuous, nowhere-differentiable function. Question: what is "sequential compactness" for a set of functions? Definitions: pointwise bounded set of functions, uniformly bounded set of functions. Remark: even if a sequence of continous functions on a compact set is uniformly bounded, there need not exist a pointwise convergent subsequence.