Hausdorff theorem about metric-space-completion
Let $(X, \rho)$ is a metric-space but not complete-metric-space. Then exists complete-metric-space $(Y, d)$ and metric-space-isometry $\pi$ so that $\pi(X)$ is dense-subset of $Y$.
Let $(X, \rho)$ is a metric-space but not complete-metric-space. Then exists complete-metric-space $(Y, d)$ and metric-space-isometry $\pi$ so that $\pi(X)$ is dense-subset of $Y$.