Ehresmann's lemma

Template:Short description In mathematics, or specifically, in differential topology, Ehresmann's lemma or Ehresmann's fibration theorem states that if a smooth mapping $f:M\to N$, 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.

See also

• Thom's first isotopy lemma

References

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