Let (X,d) be the Cartesian product of the two metric spaces (X1,d1) and (X2,d2). a) show...

Let (X,d) be the Cartesian product of the two metric spaces (X_1,d₁) and (X₂_,d₂).

a) show that a sequence {(x_n¹,x_n²)} in X is Cauchy sequence in X if and only if {x_n¹} is a Cauchy sequence in X₁ and {x_n²} is a Cauchy in X₂_.

b) show that X is complete if and only if both X₁ and X₂ are complete.

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Expert Solution

Colby Messinger answered 1 month ago

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