\begin{definition}[Definition:Completely Metrizable Topology]
Let $\struct {S, \tau}$ be a topological space.
The space $\struct {S, \tau}$ is said to be '''completely metrizable''' {{iff}} there exists a metric $d$ such that:
:$\struct {S, d}$ is a complete metric space
and:
:$\tau$ is the topological space induced by the metric $d$.
== Also see ==
{{ExtractTheorem|Trivial, but the following statement needs to be justified in its own page}}
All completely metrizable topologies are in particular metrizable topologies. 
Category:Definitions/Topology
Category:Definitions/Metric Spaces
\end{definition}