Let $(X,d)$ be a metric space and $(\bar{X},\bar{d})$ its completion. There is a list of topological properties Wikipedia - Topological property

Does anybody know list which of them are retained (inherited) for completion? For example

1. if $(X,d)$ is locally compact space then $\bar{X}$ may be non-locally compact space.
2. if $(X,d)$ is separable space then $\bar{X}$ is separable space.
3. if $(X,d)$ is connected space then $\bar{X}$ is connected space.
4. if $(X,d)$ is path-connected space then $\bar{X}$ is path-connected space.

I am interested in this problem in general, especially for the spaces with intrinsic metric.