Definition:Unit Sphere/Topology

Definition

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

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

Intuitively, it is the skin of the open $1$-ball of $\mathbb 0$ in $\R^{n + 1}$.

Sources

• 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{III}$: Metric Spaces: $n$-Spheres
• 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $2$: Metric Spaces: $\S 7$: Subspaces and Equivalence of Metric Spaces: Example $3$