    v         v
|    T_f(x) (Y)  o--------&gt;o  F
|
| [NB.  f'_V,U (x) = Df_V,U (x), as an alternate notation.]
|
| The map T_x f is obviously continuous and linear
| for the structure of topological vector space
| which we have placed on T_x (X) and T_f(x) (Y).
|
| As a matter of notation, we shall sometimes write f_*,x instead of T_x f.
|
| The operation 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).
