The following question seems trivial, but I want to make sure I do not have a mistake. Suppose I have $X,Y$ metric spaces. Denote $\overline{X\times Y}$ the completion of the product. If $\overline{X}$ and $\overline{Y}$ are the completions of each individual space, is it true to say that $\overline{X\times Y}=\overline{X}\times \overline{Y}$?
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What metric are you putting on the product? – Eric Wofsey Dec 30 '15 at 08:50
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Let's say the max of the two metrics – User666x Dec 30 '15 at 08:51
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http://math.stackexchange.com/questions/543791/the-closure-of-a-product-is-the-product-of-closures – Nigel Overmars Dec 30 '15 at 09:23
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Nigel, is this equivalent to what I asked here? I am not 100% sure. – User666x Dec 30 '15 at 12:04