Ehresmann's lemma

In mathematics, or specifically, in differential topology, Ehresmann's lemma or Ehresmann's fibration theorem states that if a smooth mapping $$ f\colon M \rightarrow N$$, 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.