  We show that a topometric space $X$ is topometrically isomorphic to a type
space of some continuous first-order theory if and only if $X$ is compact and
has an open metric (i.e., satisfies that $\{p : d(p,U) < \varepsilon\}$ is open
for every open $U$ and $\varepsilon > 0$). Furthermore, we show that this can
always be accomplished with a stable theory.
