# Definition:Open Set/Pseudometric Space

Let $P = \left({A, d}\right)$ be a pseudometric space.
An open set in $P$ is defined in exactly the same way as for a metric space:
$U$ is an open set in $P$ if and only if:
$\forall y \in U: \exists \epsilon \left({y}\right) > 0: B_\epsilon \left({y}\right) \subseteq U$
where $B_\epsilon \left({y}\right)$ is the open $\epsilon$-ball of $y$.