Let $X$ be a metric space and $\hat{X}$ its completion. Show that $\hat{X}$ is a Banach space.
I think this is false, but I can't find a counterexample.
2026-04-03 04:43:12.1775191392
Completion of a Metric Space is Banach Space?
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Take any complete metric space which is not a Banach space (such as $S^1$, endowed with the usual topology), which will then be homeomorphic to its completion. Therefore, it will not be a Banach space.