Definition:Open Set/Pseudometric Space

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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 $P$ if and only if:

$\forall y \in U: \exists \map \epsilon y > 0: \map {B_\epsilon} y \subseteq U$

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