n T satisfies an obvious functorial property,
| namely, if f : X -&gt; Y and g : Y -&gt; Z are morphisms, then
|
| T_x(g o f)  =  T_f(x)(g) o T_x(f).
|
| T_x(id)     =  id.
|
| We may reformulate Proposition 2.2:
|
| Proposition 2.3.  Let X, Y be manifolds of class C^p (p &gt;= 1) modeled on Banach spaces.
|
|                   Let f : X -&gt; Y be a C^p-morphism.  Let x be in X.  Then:
|
|                   1.  f is an immersion at x if and only if
|
|                       the map T_x f is injective and s