Metrization of Regular Second Countable Space

Theorem
Let $T = \struct {S, \tau}$ be a $T_1$ space.


 * $(1): \quad T$ is regular and second-countable
 * $(2): \quad T$ is homeomorphic to a metric subspace of the Hilbert cube $I^\omega$
 * $(3): \quad T$ is metrizable and separable

Also known as
In some sources this theorem is known as Urysohn's Metrization Theorem as it includes the sufficient condition to the necessary conditions of metrization that is the subject of what is more commonly known as Urysohn's Metrization Theorem.

Also see

 * Urysohn's Metrization Theorem