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:

$\map { {B_R}^-} a = \set {x \in \R^n : \norm {x - a} \le R}$

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Also see

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

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): ball
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): ball