List questions from diffeomorphism

Published on 22 Mar 2026 - 5:28

1.9k

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Is every diffeomorphism an open map?

Published on 22 Mar 2026 - 9:30

202

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One line proof - the jacobian is sometimes $1$ or $-1$

Published on 07 Apr 2018 - 14:12

476

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Twice contracted Bianchi identity from diffeomorphism invariance

Published on 20 Mar 2026 - 10:42

198

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Persistence of elliptic / parabolic fixed points of maps and flows

Published on 22 Mar 2026 - 13:09

263

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Show $\mathbb{R}^n$ is not diffeomorphic to $\mathbb{R}^m$ for $m\neq n$

Published on 15 May 2018 - 14:12

45

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Need a counter example for tangent map preserving inner product, but F is not isometry

Published on 16 May 2018 - 7:51

149

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How do I set up Implicit Function Theorem to verify this function is a $C^{r}$ diffeomorphism?

Published on 22 Mar 2026 - 1:04

63

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In $\Bbb R^3$, If tangent map of F preserves inner product, then F is an isometry?

Published on 26 May 2018 - 16:42

146

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Structural stability in orientation preserving $[0,1]$ diffeomorphism

Published on 28 May 2018 - 20:46

1.5k

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$F$ is local diffeomorphism $\Leftrightarrow$ $F$ preserves or reverses orientation.

Published on 08 Jun 2018 - 21:59

363

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Proof that $\text{Diff}(M)$ is a topological group

Published on 28 Jun 2018 - 19:50

133

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Definition of hyperbolic set in dynamical systems

Published on 22 Mar 2026 - 15:22

70

Views

Level curve and PDE

Published on 21 Mar 2026 - 19:31

52

Views

How to show that $[c_i, d_i] \subset [a_i- \lambda, b_i + \lambda]$?

Published on 13 Jul 2018 - 10:33

List Question

Interpretation for diffeomorphism

Is every diffeomorphism an open map?

One line proof - the jacobian is sometimes $1$ or $-1$

Twice contracted Bianchi identity from diffeomorphism invariance

Persistence of elliptic / parabolic fixed points of maps and flows

Show $\mathbb{R}^n$ is not diffeomorphic to $\mathbb{R}^m$ for $m\neq n$

Need a counter example for tangent map preserving inner product, but F is not isometry

How do I set up Implicit Function Theorem to verify this function is a $C^{r}$ diffeomorphism?

In $\Bbb R^3$, If tangent map of F preserves inner product, then F is an isometry?

Structural stability in orientation preserving $[0,1]$ diffeomorphism

$F$ is local diffeomorphism $\Leftrightarrow$ $F$ preserves or reverses orientation.

Proof that $\text{Diff}(M)$ is a topological group

Definition of hyperbolic set in dynamical systems

Level curve and PDE

How to show that $[c_i, d_i] \subset [a_i- \lambda, b_i + \lambda]$?

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