Definition:Closed Disk

Definition

Let $V$ be a vectorspace and $x \in V$, $r \in \R$. Then the closed disk $\bar{D}$ centered at $x$ with radius $r$ is the set:

$\bar{D}(x, r) := \{v \in V | \| x - v \| \le r\}$

Remarks

• $\| \cdot \|$ is a norm over $V$.
• The word disk usually implies that $V$ has two dimensions. In higher dimensions sphere or ball are more commonly used to describe this set.
• See also Definition:Closed Ball