x such that the composite map
|
|     f        r                pr
| U -----&gt; V -----&gt; V_1 x V_2 ------&gt; V_2
|
| is a submersion.
|
| In particular, if f is transversal over W, then f^-1(W) is a submanifold of X,
| because the inverse image of 0 by our local composite map
|
| pr o r o f
|
| is equal to the inverse image of W |^| V by r.
|
| Lang, DARM, page 27.

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

| 2.  Manifolds
|
| 2.1.  Atlases, Charts, Morphisms
|
| Let X be a set.  An &