V,U(x)v.
| The representation of T_x f on the spaces of charts can
| be given in the form of a diagram
|
|       T_x(X)  o--------&gt;o   E
|               |         |
|       T_x f   |         |   f'_V,U(x)
|               v         v
|    T_f(x)(Y)  o--------&gt;o   F
|
| 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 operatio