Ehresmann's lemma explained

f\colon M → N , where M and N are smooth manifolds, is

1. a surjective submersion, and
2. a proper map (in particular, this condition is always satisfied if M is compact),

then it is a locally trivial fibration. This is a foundational result in differential topology due to Charles Ehresmann, and has many variants.

See also

• Thom's first isotopy lemma

References

• • Book: Kolář. Ivan. Michor. Peter W.. Slovák. Jan. Natural operations in differential geometry. Springer-Verlag. Berlin. 1993. 3-540-56235-4. 1202431. 0782.53013.