Definition:Sphere/Normed Division Ring/Center

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 $S_\epsilon \paren{a}$ be the $\epsilon$-sphere of $a$.

In $S_\epsilon \paren{a}$, the value $a$ is referred to as the center of the $\epsilon$-sphere.