Definition:Unit Sphere/Normed Vector Space

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 $1$:


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