# Definition:Sphere/Topology/Unit Sphere

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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 $\R^{n+1}$.