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