Definition:Open Set/Pseudometric Space

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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 $y$.