Construction of Manifold in ${\mathbb{R}}^2$

Example

Example. {Youtube - whybmaths} Construction of a manifold in ${\mathbb{R}}^2$. Let $({\mathbb{R}}^2,{\tau }_{{\mathbb{R}}^2})$ be a Topological Space and let $\mathcal{A}=(U_{\alpha },{\phi }_{\alpha })$ an be Atlas 1, where the coordinate chart is the the identity map.