\begin{definition}[Definition:Pseudometrizable Topology]
Let $\left({S, d}\right)$ be a pseudometric space.
Let $\left({S, \tau_d}\right)$ 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'''.
\end{definition}