Hi,

I'm trying to show that there is a bijection between the set of sections of a smooth vector bundle and the set of smooth vector bundle morphisms from the trivial line bundle to .

Since I can't draw a diagram here, the morphisms are given so that (hopefully that makes sense).

Given a section , I get a morphism by .

Given a morphism, I get a section by .

However this does not seem to give a bijection, since sending a morphism to a section and back to a morphism I get for any which doesn't seem right.

Any help would be greatly appreciated, as I have a paper due over Easter.