Atlas on \(\mathbb{R}^n\)

\[ \DeclareMathOperator{\id}{id} \]

The global chart \( (\mathbb{R}^n, \id_{\mathbb{R}^n}) \) is an atlas on \( \mathbb{R}^n \).

Remarks

This atlas is smooth, since every atlas containing exactly on chart is smooth by definition.
This atlas determines the standard smooth structure on \(\mathbb{R}^d\) .