 we let g : U -&gt; V_2 be the map pi o f, where
|         pi is the projection, and note that our assumption means that g'(0) is
|         surjective and its kernel splits.  Furthermore, g^-1(0) = f^-1(W).
|         We can then use Corollary 5.7 of the inverse mapping theorem
|         to conclude the proof.
|
| Lang, DARM, pages 27-28.

¤~~~~~~~~~¤~~~~~~~~~¤~SYLLABUS~¤~~~~~~~~~¤~~~~~~~~~¤

| 2.  Manifolds
|
| 2.1.  Atlases, Charts, Morphisms
|
| Let X be a set.  An &quot;atlas of class C^p (p &gt;= 