Let \(\mathbb{S}^n\) denote the \(n\)-sphere . Then, \(\mathbb{S}^n\) is a manifold , since \(\mathbb{S}^n\) is as a subspace of \(\mathbb{R}^{n+1}\) Hausdorff and second-countable. It is locally Euclidean since it has an atlas (see (0x68f36f7f) ).
Let \(\mathbb{S}^n\) denote the \(n\)-sphere . Then, \(\mathbb{S}^n\) is a manifold , since \(\mathbb{S}^n\) is as a subspace of \(\mathbb{R}^{n+1}\) Hausdorff and second-countable. It is locally Euclidean since it has an atlas (see (0x68f36f7f) ).