Let \(\phi\colon M\to N\) be a smooth map between two smooth manifolds with constant rank . Then every level set of \(\phi\) is an embedded submanifold on \(M\) whose codimension is equal to the dimension of \(N\). [@lee2013smooth_manifolds, Theorem 5.12]
Remarks
- this implies that the level sets of every smooth submersion are embedded submanifolds