\begin{definition}[Definition:Closed Ball/P-adic Numbers]
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.
The '''closed $\epsilon$-ball of $a$ in $\struct {\Q_p, \norm {\,\cdot\,}_p }$''' is defined as:
:$\map { {B_\epsilon}^-} a = \set {x \in R: \norm {x - a}_p \le \epsilon}$
\end{definition}