Boundary Set

A (symmetrical) boundary set of Radius $r$ and center ${\bf x}_0$ is the set of all points ${\bf x}$ such that

$$\vert{\bf x}-{\bf x}_0\vert = r.$$

Let ${\bf x}_0$ be the Origin. In $\Bbb{R}^1$, the boundary set is then the pair of points $x = r$ and $x = -r$. In $\Bbb{R}^2$, the boundary set is a Circle. In $\Bbb{R}^3$, the boundary set is a Sphere.

See also Circle, Disk, Open Set, Sphere