Definition:Open Set/Pseudometric Space

Definition
Let $P = \struct {A, d}$ 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 $P$ :
 * $\forall y \in U: \exists \map \epsilon y > 0: \map {B_\epsilon} y \subseteq U$

where $\map {B_\epsilon} y$ is the open $\epsilon$-ball of $y$.