\begin{definition}[Definition:Open Ball]
Let $M = \struct {A, d}$ be a metric space or pseudometric space.
Let $a \in A$.
Let $\epsilon \in \R_{>0}$ be a strictly positive real number.
The '''open $\epsilon$-ball of $a$ in $M$''' is defined as:
:$\map {B_\epsilon} a := \set {x \in A: \map d {x, a} < \epsilon}$
If it is necessary to show the metric or pseudometric itself, then the notation $\map {B_\epsilon} {a; d}$ can be used.
\end{definition}