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Assume that (X, dX) and (Y, dY ) are complete spaces, and give X × Y...

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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