Question

Asked Nov 1, 2019

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2. Assume that (X, d_{X)} and (Y, d_{Y} ) are complete spaces, and give X × Y the

metric d defined by

d((x_{1}, y_{1}),(x_{2}, y_{2})) = dX(x_{1}, x_{2}) + dY (y_{1}, y_{2})

Show that (X × Y, d) is complete.

Step 1

To prove that every Cauchy sequence in the product space XxY converges (under the metric defined in the problem)

Step 2

Statement to be proved

Step 3

First prove that the projections of any Cauchy sequenc...

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