Let $i:N\to M$ be a smooth embedding, $\pi:E\to N$ a vector bundle and $s_0:N\to E$ its zero section.
I have an open neighborhood $U$ of $s_0(N)$ in $E$, and $f:U\to M$ is a smooth map such that $f\circ s_0=i$ and $T_xf$ is bijective for any $x\in s_0(N)$.
How could I prove that there exists an open neighborhood $V$ of $s_0(N)$ in $U$ such that $f|_V$ is a diffeomorphism onto its image?
Constructing a diffeomorphism
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differential-geometry
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0@S.L.: Thanks, I'll prove to adapt the last three paragraphs in the proof at page $2$56 of Lee, as you adressed to me. – 2011-02-14