(a) In  defineShow that d′ is a metric that induces the usual topology of  Sketch the basi...

(a) In  define

Show that d′ is a metric that induces the usual topology of  Sketch the basis elements under d′ when n = 2.

(b) More generally, given p ≥ 1, define

for . Assume that d′ is a metric. Show that it induces the usual topology on