Definition:Open Set/Pseudometric Space

Definition
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 $P$ iff:
 * $\forall y \in U: \exists \epsilon \left({y}\right) > 0: B \left({y; \epsilon \left({y}\right)}\right) \subseteq U$

where $B \left({y; \epsilon \left({y}\right)}\right)$ is the open $\epsilon$-ball of $y$.