Let denotes the collection of all bounded functions from a closed interval [a,b] into R. Let be a metric for such that .

Let denotes the collection of all continuous real-valued functions on [a,b] such that is a closed subspace of .

Let be a metric for such that .

(a) Show that is not a compact in .

(b) Show that is no where dense in .

(c) A sequence in converges to a member with respect to the metric if and only if converges to f uniformly.