# Open Subset

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.

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#### Solution Summary

Metric Space is typified.

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