In mathematics, particularly in the field of differential topology, the preimage theorem is a variation of the implicit function theorem concerning the preimage of particular points in a manifold under the action of a smooth map.

Statement of Theorem

Definition. is a regular value of is surjective are the tangent spaces

Theorem. then the codimension Also, the tangent space

There is also a complex version of this theorem:

Theorem. be two complex manifolds be a holomorphic

See also

References