Definition:Sphere/Metric Space/Center

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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.