Definition:Sphere/P-adic Numbers/Center

Definition
Let $p$ be a prime number.

Let $\struct {\Q_p, \norm {\,\cdot\,}_p}$ be the $p$-adic numbers.

Let $a \in \Q_p$.

Let $\epsilon \in \R_{>0}$ be a strictly positive real number.

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

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