Definition:Topologically Complete Space

Definition
Let $T = \struct {S, \tau}$ be a topological space.

Let $M = \struct {S, d}$ be a complete metric space such that $\struct {S, \tau}$ 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