Definition:Closed Unit Ball

This page is about closed unit ball. For other uses, see Ball.

Definition

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

Let $a \in X$.

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

$\map {B_1^-} a := \set {x \in X: \norm {x - a} \le 1}$

Sources

• 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): $\S 1.2$: Normed and Banach spaces. Normed spaces