Definition:Completely Metrizable Topology
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Definition
Let $\struct {S, \tau}$ be a topological space.
The space $\struct {S, \tau}$ is said to be completely metrizable if and only if 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
- Results about completely metrizable topologies can be found here.