Definition:Sphere/Metric Space/Radius

Definition
Let $M = \left({A, d}\right)$ be a metric space or pseudometric space.

Let $a \in A$.

Let $S_\epsilon \left({a}\right)$ be the $\epsilon$-sphere of $a$.

In $S_\epsilon \left({a}\right)$, the value $\epsilon$ is referred to as the radius of the $\epsilon$-sphere.

Caution
It should be noted that the radius is not intrinsic to the $\epsilon$-sphere, so that the radius of a sphere is ambiguous.