plits.
|
|                   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.
|
| If W is a submanifold of a manifold Y of class C^p (p &gt;= 1), then the inclusion
|
| i : W -&gt; Y
|
| induces a map
|
| T_w i : T_w(W) -&gt; T_w(Y)
|
| which is in fact an i