*4, Let U be an open subset of R" and f:U-R" a function whose component functions have continuous partial derivatives. We say that f is an immersion if Dsf is injective for all v in U...

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*4, Let U be an open subset of R and f:U-R a function whose component functions have continuous partial derivatives. We say

containing f), and a diffeomorphism h of W onto an open subset of R such that

*4, Let U be an open subset of R" and f:U-R" a function whose component functions have continuous partial derivatives. We say that f is an immersion if Dsf is injective for all v in U and a submersion if Dof is surjective for allv in U. (a) Suppose that f:U-R" is an immersion. Prove that, for each v in U, we can find an open set V of U containing v, an open set W of R" containing f (v), and a diffeomorphism h of W onto an open subset of R" such that (b) Suppose that f: U R" is a submersion. Prove that, for each v n U, we can find an open subset V of U containing V, an open subset W of R
containing f), and a diffeomorphism h of W onto an open subset of R" such that

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*4, Let U be an open subset of R" and f:U-R" a function whose component functions have continuous partial derivatives. We say that f is an immersion if Dsf is injective for all v in U...

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*4, Let U be an open subset of R" and f:U-R" a function whose component functions have continuous partial derivatives. We say that f is an immersion if Dsf is injective for all v in U...

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Add Answer to: *4, Let U be an open subset of R" and f:U-R" a function whose component functions have continuous partial derivatives. We say that f is an immersion if Dsf is injective for all v in U...

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*4, Let U be an open subset of R" and f:U-R" a function whose component functions have continuous partial derivatives. We say that f is an immersion if Dsf is injective for all v in U...