Exercise 6.7.3. Let f: Rⁿ → Rⁿ be a continuously differentiable function such that f'(c) is an invertible linear transformation for every c ∈ Rⁿ. Show that whenever V is an open set in Rⁿ, f(V) is also open. Hint: use the inverse function theorem.
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We are given that $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$ is a continuously differentiable function. Show more…
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