Submetrizable space

Definition
A topological space is said to be submetrizable if it is either a metrizable space to begin with or we can choose a coarser topology on the space and thus make it a metrizable space.

Metaproperties
This follows from the fact that a direct product of metrizable spaces is metrizable.

This follows from the fact that any subspace of a metrizable space is metrizable.

This follows immediately from the definition.