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.
To prove that every Cauchy sequence in the product space XxY converges (under the metric defined in the problem)
Statement to be proved
First prove that the projections of any Cauchy sequenc...
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