Definition:Closed Ball/P-adic Numbers/Center

Definition
Let $p$ be a prime number.

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

Let $a \in R$.

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

Let ${B_\epsilon}^- \paren{a}$ be the closed $\epsilon$-ball of $a$.

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