Let \(\mathbb{S}^n\) denote the \(n\)-sphere . Then, \(\mathbb{S}^n\) is
- connected ,
- a quotient space of \(\mathbb{R}^{n+1}\setminus \{0\}\) ,
- compact,
- a manifold ,
- \(\mathbb{S}^n\) is a compact analytic manifold.
Remark
- All properties also hold for non-unit \(n\)-spheres.