Show that the metrics d(f,g) = intergral 0 to 1 abs (f(t) - g(t) dt and

d'(f,g) = max {abs f(t) - g(t) : t in [0,1] on the set C[0,1] of continuous real valued functions on [0,1] are not topologically equivalent.

Hint: If d' is topologically equivalent to d, then a sequence {Xn} converges to X in one metric iff it converges to X in the other metric.

Thanks.