Definition:Metrizable Topology/Definition 1

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

$T$ is said to be metrizable there exists a metric $d$ on $S$ such that:
 * $\tau$ is the topology induced by $d$ on $S$.

Also see

 * Definition:Metrizable Topology/Definition 2


 * Equivalence of Definitions of Metrizable Topology


 * Indiscrete Topology is not Metrizable: thus, not all topological spaces are metrizable


 * Definition:Completely Metrizable Topology