2. Assume that (X, dX) and (Y, dY ) are complete spaces, and give X × Y themetric d defined byd((x1, y1),(x2, y2)) = dX(x1, x2) + dY (y1, y2)Show that (X × Y, d) is complete.

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2. Assume that (X, dX) and (Y, dY ) are complete spaces, and give X × Y the
metric d defined by
d((x1, y1),(x2, y2)) = dX(x1, x2) + dY (y1, y2)
Show that (X × Y, d) is complete.

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