Definition:Open Ball/Radius

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

Let $a \in A$.

Let $B_\epsilon \left({a}\right)$ be the open $\epsilon$-ball of $a$.

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

Caution
It should be noted that the radius is not intrinsic to the open ball, so that the radius of an open ball is ambiguous.