Definition:Sphere/Topology

Definition

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

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

where $\size {\, \cdot \, }$ denotes the Euclidean distance.

Radius

The radius of an $n$-sphere:

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

is the value $r$.

Center

The center of an $n$-sphere:

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

is the point $y \in \R^{n + 1}$.

Also see

• Results about spheres in the context of topology can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): sphere
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): sphere