\begin{definition}[Definition:Open Ball/P-adic Numbers]
Let $p$ be a prime number.
Let $\struct {\Q_p, \norm {\,\cdot\,}_p}$ be the $p$-adic numbers.
Let $a \in R$.
Let $\epsilon \in \R_{>0}$ be a strictly positive real number.
The '''open $\epsilon$-ball of $a$ in $\struct {\Q_p, \norm {\,\cdot\,}_p}$''' is defined as:
:$\map {B_\epsilon} a = \set {x \in \Q_p: \norm{x - a}_p < \epsilon}$
\end{definition}