tion as in AT 3) is a C^p-isomorphism.
|
| Two atlases are said to be &quot;compatible&quot; if each chart of one is compatible with
| the other atlas.  One verifies immediately that the relation of compatibility
| between atlases is an equivalence relation.  An equivalence class of atlases
| of class C^p on X is said to define a structure of &quot;C^p-manifold&quot; on X.
|
| If all the vector spaces E_i in some atlas are toplinearly isomorphic, then we can always
| find an equivalent atlas for which they 