List questions from inverse-function-theorem

Published on 26 Mar 2026 - 1:45

83

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For any point in $\Bbb R^2$ $f$ has a local inverse. Can I say $f$ is invertible on its range?

Published on 26 Mar 2026 - 10:15

208

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Assumption in prooving the Inverse Function Theorem (in Spivak's "Calculus on manifolds")

Published on 26 Mar 2026 - 11:45

122

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Prove that there is an $n \times n$ matrix $B$ such that $A=B^{2}+B .$

Published on 26 Mar 2026 - 15:55

62

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Surface in $\mathbb{R}^3$ implicitely defined by a $C^1$-function is locally similar to $xy$-plane

Published on 26 Mar 2026 - 10:57

47

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Explaining an incorrect solution involving derivative of an inverse.

Published on 25 Mar 2026 - 19:12

134

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If $\varphi(x,y)=(x+f(y),y+f(x))$ with $|f'(t)|\le k<1$ for all $t\in\mathbb{R}$, then $\varphi$ is a diffeomorphism

Published on 26 Mar 2026 - 10:44

107

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connected components of domain without preimage of critical values

Published on 26 Mar 2026 - 14:32

76

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Global invertibility of a given function

Published on 25 Mar 2026 - 18:50

91

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Reference request: Variations of inverse function theorem

Published on 26 Mar 2026 - 9:08

213

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How can I get an intuition about Copula?

Published on 23 Feb 2026 - 15:48

54

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Compute $Df^{-1}(2,5)$ given $f(u,v)=(uv,u^2+v^2)$ using the Inverse Function Theorem (IFT)

Published on 25 Mar 2026 - 19:05

51

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Proof of continuity of a map from product of two spaces to $\mathbb R^n.$

Published on 04 Apr 2021 - 16:05

183

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Is this result true? Uniform convergence and inverses

Published on 25 Mar 2026 - 22:37

116

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Application of the inverse function theorem on a convex set

Published on 27 Mar 2026 - 1:50

List Question

How do I find the Inverse of $f(x)$?

For any point in $\Bbb R^2$ $f$ has a local inverse. Can I say $f$ is invertible on its range?

Assumption in prooving the Inverse Function Theorem (in Spivak's "Calculus on manifolds")

Prove that there is an $n \times n$ matrix $B$ such that $A=B^{2}+B .$

Surface in $\mathbb{R}^3$ implicitely defined by a $C^1$-function is locally similar to $xy$-plane

Explaining an incorrect solution involving derivative of an inverse.

If $\varphi(x,y)=(x+f(y),y+f(x))$ with $|f'(t)|\le k<1$ for all $t\in\mathbb{R}$, then $\varphi$ is a diffeomorphism

connected components of domain without preimage of critical values

Global invertibility of a given function

Reference request: Variations of inverse function theorem

How can I get an intuition about Copula?

Compute $Df^{-1}(2,5)$ given $f(u,v)=(uv,u^2+v^2)$ using the Inverse Function Theorem (IFT)

Proof of continuity of a map from product of two spaces to $\mathbb R^n.$

Is this result true? Uniform convergence and inverses

Application of the inverse function theorem on a convex set

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