f the integer p (which may also be infinity) is fixed throughout a discussion,
| we also say that X is a manifold.
|
| Lang, DARM, page 21.
|
| Let X be manifold, and U an open subset of X.  Then it is possible,
| in the obvious way, to induce a manifold structure on U, by taking
| as charts the intersections
|
| (U_i |^| U, q_i | (U_i |^| U)).
|
| [Notation.  &quot;f | S&quot; indicates the function f as restricted to the set S.]
|
| If X is a topological space, covered by open subsets V_j, and if we are
|