In mathematics, or specifically, in differential topology, Ehresmann's lemma or Ehresmann's fibration theorem states that if a smooth mapping f : M → N {\displaystyle f\colon M\rightarrow N} , where M {\displaystyle M} and N {\displaystyle 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.