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
  1. a surjective submersion, and
  2. a proper map,,
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.