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 $\overline{X\times Y}=\overline{X}\times \overline{Y}$?
2026-03-28 02:06:38.1774663598
is finite product of complete metric spaces is the same as completion of finite product?
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