Definition:Sphere/Normed Vector Space/Radius

Definition
Let $\struct{X, \norm{\,\cdot\,}}$ be a normed vector space.

Let $x \in X$.

Let $\epsilon \in \R_{>0}$ be a strictly positive real number.

Let $\map {S_\epsilon} x$ be the $\epsilon$-sphere of $x$.

In $\map {S_\epsilon} x$, the value $\epsilon$ is referred to as the radius of the $\epsilon$-sphere.