Definition:Closed Ball

P-adic Numbers
The definition of an closed ball in the context of the $p$-adic numbers is a direct application of the definition of a closed ball in a normed division ring:

Also denoted as
The notation $\map {B^-} {a; \epsilon}$ can be found for $\map { {B_\epsilon}^-} a$, particularly when $\epsilon$ is a more complicated expression than a constant.

Similarly, some sources allow $\map { {B_d}^-} {a; \epsilon}$ to be used for $\map { {B_\epsilon}^-} {a; d}$.

It needs to be noticed that the two styles of notation allow a potential source of confusion, so it is important to be certain which one is meant.

Also see

 * Definition:Open Ball of Metric Space