Definition:Sphere/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 $\epsilon$-sphere of $a$ in $\struct {\Q_p, \norm {\,\cdot\,}_p}$ is defined as:


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

Also see

 * Definition:Open Ball in P-adic Numbers


 * Definition:Closed Ball in P-adic Numbers


 * P-adic Sphere is Instance of Sphere of a Norm