Definition:Closed Ball/Real Analysis

Definition
Let $n \ge 1$ be a natural number.

Let $\R^n$ denote real Euclidean space

Let $\norm{\, \cdot \,}$ denote the Euclidean norm.

Let $a \in \R^n$.

Let $R > 0$ be a strictly positive real number.

The closed ball of center $a$ and radius $R$ is the subset:
 * $\map { {B_R}^- } a = \set{x \in \R^n : \norm{x - a} \le R }$

Also see

 * Definition:Open Ball of Real Euclidean Space
 * Definition:Closed Set (Real Analysis)