# Definition:Sphere/Metric Space/Center

## Definition

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

Let $a \in A$.

Let $S_\epsilon \paren{a}$ be the $\epsilon$-sphere of $a$.

In $S_\epsilon \paren{a}$, the value $a$ is referred to as the **center** of the $\epsilon$-sphere.

## 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

*This article incorporates material from sphere (metric space) on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.*