Definition:Closed Ball/P-adic Numbers

Definition
Let $p$ be a prime number.

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

Let $a \in \Q_p$.

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:


 * $\map { {B_\epsilon}^-} a = \set {x \in R: \norm {x - a}_p \le \epsilon}$

Also see

 * Definition:Open Ball in P-adic Numbers
 * Definition:Sphere in P-adic Numbers
 * P-adic Closed Ball is Instance of Closed Ball of a Norm