Really need help with manifolds.
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.
Would really appreciate some help, cookies for anyone who can give me a hand :)

Question

Really need help with manifolds.
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.
Would really appreciate some help, cookies for anyone who can give me a hand :)

experimentx · Answer

what are you doing dude?? try posting it here http://math.stackexchange.com/

anonymous · Answer

lol what do you call this" sets and  group theory"

anonymous · Answer

topolgy

anonymous · Answer

thanks forthe link @experimentX

anonymous · Answer

Thanks @experimentX I'll give it a go.