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.

Linguistic Note
The plural of radius is radii, pronounced ray-dee-eye.

This irregular plural form stems from the Latin origin of the word radius, meaning ray

The ugly incorrect form radiuses can apparently be found, but rarely in a mathematical context.