Let (X_i, d_i) be metric spaces. Let X=X_1 x X_2 x .... x X_n and let (X,d) be the- metric space defined in the standard manner : d(x,y)=max(d_i(x_i,y_i)) . For i = 1,2,...n , let O_i be an open subset of X_i. Prove that the subset O_1 x O_2 x ... x O_n of X is open and that each subset of X is a union of sets of this form.© BrainMass Inc. brainmass.com October 10, 2019, 1:41 am ad1c9bdddf
Metric Space is typified.