Let (X, dX ) and (Y , dY ) be metric spaces. The product of X and Y (written X × Y ) is the set of pairs {(x, y) : x ∈ X, y ∈ Y } with the metric:(adsbygoogle = window.adsbygoogle || []).push({});

d((x1 , y1 ), (x2 , y2 )) = max {dX (x1 , x2 ), dY (y1 , y2 )}

1)How to prove that d is a metric on X × Y?

2)Prove that d induces the product topology on X × Y.

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# Product of Two Metric Spaces

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