a) Prove that the metric space C[a, b] in Example 10.6 is complete.
b) Let ||f||1: = ∫ba |f(x)|dx and define
dist(f, g) := ||f - g||1
for each pair f, g ∈ C[a, b]. Prove that this distance function also makes C[a, b] a metric space.
c) Prove that the metric space C[a, b] defined in part b) is not complete.