Is locally completeness a topological property? – math.stackexchange.com

Is locally completeness a topological property? – math.stackexchange.com

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I know that completeness itself is not a topological property because a complete and a not complete metric space can be homeomorphic, e.g. $\Bbb R$ and $(0,1)$. However, both $\Bbb R$ and $(0,1)$ are ...

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