: Matemáticas: Ehresmann's lemma

topology > differential topology > Ehresmann's lemma

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)

http://data.loterre.fr/ark:/67375/PSR-PGBQRNQ4-L

RDF/XML TURTLE JSON-LD Creado 2/8/23, última modificación 3/8/23

Loterre