Let \(X\) be a topological space . A collection of local charts \((\Omega_i, \varphi_i)_{i \in I}\) which satisfies \(\bigcup_{i \in I}\Omega_i = M_n\) is called atlas.
Remark
- Atlases are essential for describing manifolds. However, since there is no unique choice for an atlas one needs to find geometric invariants which do not depend on the chosen atlas.
Examples