- #1
JYM
- 14
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I have been stuck several days with the following problem.
Suppose M and N are smooth manifolds, U an open subset of M , and F: U → N is smooth. Show that there exists a neighborhood V of any p in U, V contained in U, such that F can be extended to a smooth mapping F*: M → N with F(q)=F*(q) for all q in V. [smooth means C-infinity].
I try to use charts to get a smooth map between Euclidean spaces and I know how to extend such maps. but I get a difficulty in transforming to the original problem. If you have some hint please well come. thanks in advance.
Suppose M and N are smooth manifolds, U an open subset of M , and F: U → N is smooth. Show that there exists a neighborhood V of any p in U, V contained in U, such that F can be extended to a smooth mapping F*: M → N with F(q)=F*(q) for all q in V. [smooth means C-infinity].
I try to use charts to get a smooth map between Euclidean spaces and I know how to extend such maps. but I get a difficulty in transforming to the original problem. If you have some hint please well come. thanks in advance.