map T_x f is injective and splits.
|
|                   2.  f is a submersion at x if and only if
|
|                       the map T_x f is surjective and its kernel splits.
|
| Note.  If X, Y are finite dimensional, then the condition that T_x f splits
| is superfluous.  Every subspace of a finite dimensional vector space splits.
|
| Lang, DARM, page 26.
|
| Serge Lang,
|'Differential &amp; Riemannian Manifolds',
| Springer-Verlag, New York, NY, 1995.

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