Definition:Pseudometrizable Topology

Definition
Let $\struct {S, d}$ be a pseudometric space.

Let $\struct {S, \tau_d}$ be the topological space induced by $d$.

Then for any topological space which is homeomorphic to such a $\left({S, \tau_d}\right)$, it and its topology are defined as pseudometrizable.

Linguistic Note
The UK English spelling of this is pseudometrisable, but it is rarely found.