Definition:Open Ball/Radius

Definition
Let $M = \struct {A, d}$ be a metric space or pseudometric space.

Let $a \in A$.

Let $\map {B_\epsilon} a$ be the open $\epsilon$-ball of $a$.

In $\map {B_\epsilon} a$, 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.