Let \(M_n\) be a \(n\)-manifold . Two smooth atlases \(\mathcal{A}_1\) and \(\mathcal{A}_2\) are equivalent if the union is an smooth atlas.

Remarks
  • According to (0x68f0e23e) , if \(\mathcal{A}_1\) and \(\mathcal{A}_2\) are equivalent, they determine the same smooth structure on \(M_n\).