Complete metric space

Let $(X, \rho)$ - a metric-space.

It is considered complete if each fundamental sequence from this space converges to an element from this space.

If a space is not complete, we can build a metric-space-completion.

Properties

• If $(X, \rho)$ is complete and $S \subset X$ is a closed-set then $(S, \rho)$ is a complete metric space.