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.