Definition:Closed Ball/Normed Division Ring/Center

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Definition

Let $\struct {R, \norm{\,\cdot\,}}$ be a normed division ring.

Let $a \in R$.

Let $\epsilon \in \R_{>0}$ be a strictly positive real number.

Let $\map { {B_\epsilon}^-} a$ be the closed $\epsilon$-ball of $a$.


In $\map { {B_\epsilon}^-} a$, the value $a$ is referred to as the center of the closed $\epsilon$-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.


Sources