Question

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

score 933 · Answer 1 · 2019-03-04 00:57:57

933

Views

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

Published on 04 Mar 2019 - 0:57

score 75 · Answer 2 · 2019-03-22 20:35:50

75

Views

An application of implicit fuction theorem

Published on 22 Mar 2019 - 20:35

score 1.2k · Answer 3 · 2019-03-29 01:13:42

1.2k

Views

Why is continuous differentiability necessary for Inverse Function Theorem?

Published on 29 Mar 2019 - 1:13

score 57 · Answer 4 · 2019-04-07 21:51:27

57

Views

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

Published on 07 Apr 2019 - 21:51

score 45 · Answer 5 · 2019-04-09 22:12:42

45

Views

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

Published on 09 Apr 2019 - 22:12

score 74 · Answer 6 · 2019-04-10 16:37:36

74

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 10 Apr 2019 - 16:37

score 51 · Answer 7 · 2019-04-10 23:40:15

51

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 10 Apr 2019 - 23:40

score 80 · Answer 8 · 2019-04-14 07:33:56

80

Views

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

Published on 14 Apr 2019 - 7:33

score 140 · Answer 9 · 2026-03-22 12:52:11

140

Views

Doubt from Spivak's proof of inverse function theorem.

Published on 22 Mar 2026 - 12:52

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 601 · Answer 11 · 2019-05-08 18:08:24

601

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 08 May 2019 - 18:08

score 722 · Answer 12 · 2026-03-21 16:43:41

722

Views

"Counterexample" for the Inverse function theorem

Published on 21 Mar 2026 - 16:43

score 77 · Answer 13 · 2026-03-22 05:26:18

77

Views

Inverse function theorem.

Published on 22 Mar 2026 - 5:26

score 277 · Answer 14 · 2026-03-22 10:22:03

277

Views

set of points of local invertibility of function.

Published on 22 Mar 2026 - 10:22

score 55 · Answer 15 · 2026-03-22 14:28:07

55

Views

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

Published on 22 Mar 2026 - 14:28

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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