Definition:Disk

The open $$n \ $$ dimensional disk (or ball) is defined

$$\mathbb{D}^n = \left\{{x \in \mathbb{R}^n : |x-y|<r }\right\} \ $$,

where $$y \in \mathbb{R}^n \ $$ is called the center and $$r \in \mathbb{R}_+ \ $$ is called the radius.

The closed $$n \ $$-disk is defined

$$\mathbb{D}^n = \left\{{x \in \mathbb{R}^n : |x-y| \leq r }\right\} \ $$.

The boundary $$\partial \mathbb{D}^n = \mathbb{S}^{n-1} \ $$, the $$(n-1) \ $$ sphere.