)'.  Each chart (U, q) determines a bijection of T_x(X)
| on a Banach space, namely the equivalence class of (U, q, v) corresponds to
| the vector v.  By means of such a bijection it is possible to transport to
| T_x(X) the structure of topological vector space given by the chart, and
| it is immediate that this structure is independent of the chart selected.
|
| If U, V are open in Banach spaces, then to every morphism of class C^p (p &gt;= 1)
| we can associate its derivative Df(x).  If now f : X -&gt; Y 