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Let $M$ subset of $R^{n+p}$ be the zero set of a $C^\infty$ mapping $g:R^{n+p} \rightarrow R^{p}$. Assume that the Jacobi matrix of $g$ has rank $p$ everywhere on $M$. Show that $M$ is an $n$-dimensional manifold.

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hint: implicit function theorem – froggie Oct 14 '12 at 20:45

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