# Regular value theorem

From Diffgeom

*This article gives the statement and possibly proof of a theorem that discusses regular values, critical values, regular points or critical points of a smooth map between differential manifolds*

## Statement

Let be differential manifolds and be a regular value of a differentiable map . Then is a submanifold of .

A slightly stronger version of this result states the following: if there is an open neighbourhood of in such that the rank of the Jacobian is constant for all points in , then is a submanifold of .