Definition:Unit Sphere

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Definition



Topology

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

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


Normed Vector Space

The $n$-dimensional unit sphere, or unit $n$-sphere, is the $n$-sphere of radius $1$:

$\map {\Bbb S^n} x = \set {y \in \R^{n + 1} : \norm {x - y} = 1}$