Let \(M\) denote a [smooth \(n\)-manifold](smooth manifold.md) and let \(U\subseteq M\) be an open subset. Then
\[ \mathcal{A}_U=\{\text{smooth charts \(V,\varphi\) for \(M\) such that \(V\subseteq U\)}\} \]is a smooth atlas on \(U\). Endowed with the smooth structure determined by \(\mathcal{A}_U\) is called open submanifold of \(M\).