ONT Re: Differential And Riemannian Manifolds
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DARM. Note 6
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| 2.1. Atlases, Charts, Morphisms (concl.)
|
| 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 "local isomorphism" at x_0
| we mean an isomorphism:
|
| f : U_1 -> 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.
|
| Lang, DARM, p. 23.
|
| Serge Lang,
|'Differential & Riemannian Manifolds',
| Springer-Verlag, New York, NY, 1995.
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