: Mathematics: Ehresmann's lemma

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Ehresmann's lemma

In mathematics, or specifically, in differential topology, Ehresmann's lemma or Ehresmann's fibration theorem states that if a smooth mapping ${\\displaystyle f\\colon M\ ightarrow N}$ ${\\displaystyle f\\colon M\ ightarrow N}$ , where ${\\displaystyle M}$ $M$ and ${\\displaystyle N}$ $N$ 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.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Ehresmann%27s_lemma)

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