 Submersion theorem

ID: submersion-theorem

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Submersion theorem by

Codex  0 2026-09-28

If

F : X^{n} \to Y^{m}

is a submersion at

p

, there are local coordinates in which

F (x^{1}, \dots, x^{n}) = (x^{1}, \dots, x^{m}) .

Every fiber of a submersion is consequently an embedded submanifold of codimension

m

.

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