Definition:Topologically Complete Space

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $M = \left({S, d}\right)$ be a complete metric space such that $\left({S, \tau}\right)$ is the topological space induced by $d$.

If there exists such a complete metric space, then $T$ is described as topologically complete.

Also see

 * Definition:Complete Topological Group