Question

Proof that the inverse of an analytic function is analytic which uses only real analysis.

score 934 · Answer 1 · 2026-03-25 12:53:47

934

Views

Proof that the inverse of an analytic function is analytic which uses only real analysis.

Published on 25 Mar 2026 - 12:53

score 76 · Answer 2 · 2026-03-25 11:12:38

76

Views

An application of implicit fuction theorem

Published on 25 Mar 2026 - 11:12

score 1.2k · Answer 3 · 2026-03-25 16:05:08

1.2k

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Why is continuous differentiability necessary for Inverse Function Theorem?

Published on 25 Mar 2026 - 16:05

score 58 · Answer 4 · 2026-03-25 11:16:33

58

Views

$f(3t^3+2,et^2)=(3,6)$ for all $t\in\mathbb{R}$. Prove: $D_f(2,1)$ not invertible

Published on 25 Mar 2026 - 11:16

score 46 · Answer 5 · 2026-03-25 14:22:50

46

Views

How to prove that $F(x,y)=x+y^2+\sin(xy)$ defines implicitly a continuously differentiable function?

Published on 25 Mar 2026 - 14:22

score 75 · Answer 6 · 2026-03-25 11:16:39

75

Views

Showing that a set cannot be expressed as the local graph of a $C^1-$function over the $x-$axis or the $y-$axis near the origin.

Published on 25 Mar 2026 - 11:16

score 52 · Answer 7 · 2026-03-25 11:16:41

52

Views

How to find $\frac{\partial f}{\partial x}(a,b)$ and $\frac{\partial f}{\partial y}(a,b)$ of a implicit function?

Published on 25 Mar 2026 - 11:16

score 81 · Answer 8 · 2026-03-25 11:15:58

81

Views

A function $f\in C^1(\mathbb{R})$ with $f'(x)\not=0$ for all $x$ with no global inverse.

Published on 25 Mar 2026 - 11:15

score 141 · Answer 9 · 2026-03-25 11:10:37

141

Views

Doubt from Spivak's proof of inverse function theorem.

Published on 25 Mar 2026 - 11:10

score 43 · Answer 10 · 2026-03-25 07:40:38

43

Views

Proof of the proposition (Morse function in $\mathbb{C}$)

Published on 25 Mar 2026 - 7:40

score 602 · Answer 11 · 2026-03-25 12:54:54

602

Views

Is a differentiable (but not $C^1$) function $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$ with invertible derivative everywhere an open map?

Published on 25 Mar 2026 - 12:54

score 723 · Answer 12 · 2026-03-25 12:47:06

723

Views

"Counterexample" for the Inverse function theorem

Published on 25 Mar 2026 - 12:47

score 79 · Answer 13 · 2026-04-01 03:04:04

79

Views

Inverse function theorem.

Published on 01 Apr 2026 - 3:04

score 278 · Answer 14 · 2026-03-25 11:16:08

278

Views

set of points of local invertibility of function.

Published on 25 Mar 2026 - 11:16

score 56 · Answer 15 · 2026-03-25 11:16:15

56

Views

Proving a set is open in context of proof of a step in local Inverse Function Theorem

Published on 25 Mar 2026 - 11:16

List Question

Proof that the inverse of an analytic function is analytic which uses only real analysis.

An application of implicit fuction theorem

Why is continuous differentiability necessary for Inverse Function Theorem?

$f(3t^3+2,et^2)=(3,6)$ for all $t\in\mathbb{R}$. Prove: $D_f(2,1)$ not invertible

How to prove that $F(x,y)=x+y^2+\sin(xy)$ defines implicitly a continuously differentiable function?

Showing that a set cannot be expressed as the local graph of a $C^1-$function over the $x-$axis or the $y-$axis near the origin.

How to find $\frac{\partial f}{\partial x}(a,b)$ and $\frac{\partial f}{\partial y}(a,b)$ of a implicit function?

A function $f\in C^1(\mathbb{R})$ with $f'(x)\not=0$ for all $x$ with no global inverse.

Doubt from Spivak's proof of inverse function theorem.

Proof of the proposition (Morse function in $\mathbb{C}$)

Is a differentiable (but not $C^1$) function $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$ with invertible derivative everywhere an open map?

"Counterexample" for the Inverse function theorem

Inverse function theorem.

set of points of local invertibility of function.

Proving a set is open in context of proof of a step in local Inverse Function Theorem

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