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:


 * $\Bbb S^n = \left\{{x \in \R^{n+1} : \left\lvert{x}\right\rvert = 1}\right\}$

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