Definition:Unit Sphere/Normed Vector Space
< Definition:Unit Sphere(Redirected from 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 $1$:
- $\map {\Bbb S^n} x = \set {y \in \R^{n + 1} : \norm {x - y} = 1}$