\begin{definition}[Definition:Open Ball/Normed Division Ring]
Let $\struct{R, \norm {\,\cdot\,} }$ be a normed division ring.
Let $a \in R$.
Let $\epsilon \in \R_{>0}$ be a strictly positive real number.
The '''open $\epsilon$-ball of $a$ in $\struct {R, \norm {\,\cdot\,} }$''' is defined as:
:$\map {B_\epsilon} a = \set {x \in R: \norm{x - a} < \epsilon}$
If it is necessary to show the norm itself, then the notation $\map {B_\epsilon} {a; \norm {\,\cdot\,} }$ can be used.
\end{definition}