Definition:Sphere/Metric Space/Center
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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.