# Ehresmann's lemma

In mathematics, or specifically, in differential topology, **Ehresmann's lemma** or **Ehresmann's fibration theorem** states that a smooth mapping
where
and
are smooth manifolds such that
is

- a surjective submersion, and
- a proper map, (in particular, this condition is always satisfied if
*M*is compact),

is a locally trivial fibration. This is a foundational result in differential topology, and exists in many further variants. It is due to Charles Ehresmann.

## References

- Ehresmann, Charles (1951), "Les connexions infinitésimales dans un espace fibré différentiable",
*Colloque de topologie (espaces fibrés), Bruxelles, 1950*, Georges Thone, Liège; Masson et Cie., Paris, pp. 29–55, MR 0042768

This article is issued from
Wikipedia.
The text is licensed under Creative
Commons - Attribution - Sharealike.
Additional terms may apply for the media files.