Definition:Closed Unit Ball
Jump to navigation
Jump to search
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