- #1

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Even the most trivial example, show that [tex]T\mathbb{R}^n[/tex] is diffeomorphic to [tex]\mathbb{R}^{2n}[/tex] I am not seeing how to show. Showing that they are locally diffeomorphic is very easy, but every tangent bundle is locally diffeomorphic to the product space of the manifold with the appropriate Euclidean space. I am new to this topic so a geometrical route is preferred. For example, I know that if there exists a vector field with no zero vectors then the tangent bundle is trivial, but I don't know how to show why that is true, so that result does not help me.

Thanks!