Category:Metrizable Topologies

This category contains results about Metrizable Topologies.

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

Definition 1

$T$ is said to be metrizable if and only if there exists a metric $d$ on $S$ such that:

$\tau$ is the topology induced by $d$ on $S$.

Definition 2

$T$ 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 $A$.