Definition:Open Ball/Normed Division Ring/Radius

Definition
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.