Definition:Metrizable Topology/Definition 2

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

$T$ is said to be metrizable if and only if there exists a metric space $M = \struct{A, d}$ such that:

$T$ is homeomorphic to the topological space $\struct{A, \tau_d}$

where $\tau_d$ is the topology induced by $d$ on $A$.

Also see

  • Results about metrizable topologies can be found here.

Linguistic Note

The UK English spelling of metrizable is metrisable, but it is rarely found.