somorphism for each pair of indices i, j.
|
| Lang, DARM, page 20.
|
| Each pair (U_i, q_i) will be called a &quot;chart&quot; of the atlas.
| If a point x of X lies in U_i, then we say that (U_i, q_i)
| is a &quot;chart at&quot; x.
|
| Suppose that we are given an open subset U of X and a topological isomorphism
| q : U -&gt; U' onto an open subset of some Banach space E.  We shall say that
| (U, q) is &quot;compatible&quot; with the atlas {(U_i, q_i)} if each map q_i q^-1
| (defined on a suitable intersec