Definition:Unit Sphere/Topology

Definition
The $n$-dimensional unit sphere, or unit $n$-sphere, is the $n$-sphere of radius $1$ and center the origin:


 * $\Bbb S^n = \set {x \in \R^{n + 1} : \size x = 1}$

Intuitively, it is the skin of the open $1$-ball of $\mathbb 0$ in $\R^{n + 1}$.