Definition:Closed 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 closed $\epsilon$-ball of $a$.

In $\map { {B_\epsilon}^-} a$, the value $\epsilon$ is referred to as the radius of the closed $\epsilon$-ball.