only if f_Y is a morphism.
|
| The proof of this assertion depends on Lemma 2.1, and is trivial.
|
| Finally, we note that the inclusion of Y into X is a morphism.
|
| If Y is also a closed subspace of X, then
| we say that it is a &quot;closed submanifold&quot;.
|
| Suppose that X is finite dimensional of dimension n, and that Y
| is a submanifold of dimension m.  Then from the definition we see that
| the local product structure in the neighborhood of a point of Y can be
| expressed in terms of local coor