Definition:Closed Unit Ball

Definition
Let $V$ be a Banach space with norm $\left\Vert{\cdot}\right\Vert_V$.

The closed unit ball of $V$, denoted $\operatorname{ball} V$, is the set:


 * $\left\{{v \in V: \left\Vert{v}\right\Vert_V \le 1}\right\}$