\begin{definition}[Definition:Open Set/Pseudometric Space]
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 $P$''' {{iff}}:
:$\forall y \in U: \exists \map \epsilon y > 0: \map {B_\epsilon} y \subseteq U$
where $\map {B_\epsilon} y$ is the open $\epsilon$-ball of $y$.
Category:Definitions/Pseudometric Spaces
\end{definition}