Deducing matrix

Deducing matrix

Suppose that (M,d) and (P, d’) are metric spaces and X is a subset of M and Y is a subset of P.
If M x P is given the maximum metric D((x,y),(x’,y’))=max{d(x,x’), d'(y,y’)} show that a set of the form C x D is open in M x P if and only if it contains a product of balls of the form M_e(x) x P_e(y) – e represents epsilon – for any point (x,y) that belongs to C x D.
Deduce that C x D is open in M x P if and only if C is open in M and D open in P.
Deducing matrix