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