               The map f is transversal over W
|
|                   if and only if
|
|                   for each x in X such that f(x) lies in W,
|
|                   the composite map
|
|                           T_x(f)
|                   T_x(X) --------&gt; T_w(Y) ------&gt; T_w(Y)/T_w(W)
|
|                   with w = f(x) is surjective and its kernel splits.
|
| Proof.  If f is transversal over W, then for each point x in X such that f(x) lies in W,
|         we choose charts as in the definition, 