Definition:Open Ball/Center

This page is about Center in the context of Open Ball of Metric Space. For other uses, see Center.

Definition

Let $M = \struct {A, d}$ be a metric space or pseudometric space.

Let $a \in A$.

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.