Definition:Open Ball/P-adic Numbers

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.

The open $\epsilon$-ball of $a$ in $\struct {\Q_p, \norm {\,\cdot\,}_p}$ is defined as:


 * $\map {B_\epsilon} a = \set {x \in \Q_p: \norm{x - a}_p < \epsilon}$

Also see

 * Definition:Closed Ball in P-adic Numbers


 * Definition:Sphere in P-adic Numbers


 * P-adic Open Ball is Instance of Open Ball of a Norm