\begin{definition}[Definition:Open Ball/Normed Division Ring/Radius]
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.
Let $\map {B_\epsilon} a$ be the open $\epsilon$-ball of $a$.
In $\map {B_\epsilon} a$, the value $\epsilon$ is referred to as the '''radius''' of the open $\epsilon$-ball.
\end{definition}