Definition:Sphere

Topology
In the field of topology the concept is generalized.

The $n$-dimensional sphere, or $n$-sphere, is the set:


 * $\Bbb S^n = \left\{{x \in \R^{n+1} : \left|{x - y}\right| = r}\right\}$

where $r \in \R_+$ is called the radius of the sphere and $y \in \R^{n+1}$ is called the center of the sphere.

Frequently, the radius is taken as $1$ and the center as the origin.

Note
As the sphere is defined here, it is specified as being the surface only, that is, not the inside.