Definition:Open Ball/P-adic Numbers/Center
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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.
Let $\map {B_\epsilon} a$ be the open $\epsilon$-ball of $a$.
In $\map {B_\epsilon} a$, the value $a$ is referred to as the center of the open $\epsilon$-ball.
Linguistic Note
The British English spelling of center is centre.
The convention on $\mathsf{Pr} \infty \mathsf{fWiki}$ is to use the American English spelling center, but it is appreciated that there may be lapses.