Let $M^m$ be a $m-$manifold and $C=\{y^1,\dots,y^k:U\subset M\rightarrow \mathbb{R}\},\;k
Complete a set of functions to obtain a system.
3
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differential-geometry
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0Concerning 2), I think that after "straightening out" the given collection of maps (so that they become $x^1,\dots,x^k$ on $\mathbb R^m$), you should take $x^{k+1},\dots,x^m$ and reverse the process to plant them back onto $M$. – 2012-05-20