Definition:Unit Sphere/Normed Vector Space

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Definition

Let $\struct {X, \norm {\,\cdot\,} }$ be a normed vector space.

Let $x \in X$.


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

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