age 22.
|
| It is also convenient to have a local terminology.
| Let U be an open set (of a manifold or a Banach space)
| containing a point x_0.  By a &quot;local isomorphism&quot; at x_0
| we mean an isomorphism
|
| f : U_1 -&gt; V
|
| from some open set U_1 containing x_0 (and contained in U)
| to an open set V (in some manifold or some Banach space).
| Thus a local isomorphism is essentially a change of chart,
| locally near a given point.
|
| 2.2.  Submanifolds, Immersions, Submersions
|
| Let X be a t