List questions from smooth-functions

Published on 28 Jan 2022 - 16:29

41

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$\psi' \circ F \circ (\varphi')^{-1}$ is $C^\infty$ at $\varphi'(p)$.

Published on 04 Feb 2022 - 17:20

63

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Do test functions have smooth extensions?

Published on 06 Feb 2022 - 14:55

507

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Is the function $f(x)=\frac{\left(1-x^2+\sqrt{\left(1-x^2\right)^2}\right)}{2}e^{-\frac{x^2}{1-x^2}}$ a bump-function $\in C_c^\infty$? Diff. Eq.?

Published on 23 Feb 2026 - 6:24

243

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Generalization of differentiability/smoothness class "$C^n$" notation

Published on 19 Feb 2022 - 7:26

41

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Proving that $\lambda$ is not analytic in differential topology.

Published on 25 Feb 2022 - 1:19

68

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Smoothness of a function after integration w.r.t. one variable

Published on 27 Feb 2022 - 1:09

105

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Regarding Theorem 1.9, Conway, complex Analysis

Published on 26 Mar 2026 - 11:16

38

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What is the domain of $g^* \circ f^*$?

Published on 01 Mar 2022 - 14:21

67

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For a Lie-group G and embedded Lie-subgroups K < H < G, prove that $\pi:G/K \rightarrow G/H$ is a surjective smooth submersion

Published on 06 Mar 2022 - 16:40

172

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Mathematical Definition of "Smoothness" : Requirement of Differentiable Functions to be Smooth?

Published on 08 Mar 2022 - 17:13

361

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Smooth Atlas of a Smooth Manifold

Published on 09 Mar 2022 - 23:01

323

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How to prove product and quotient of smooth functions is smooth

Published on 12 Mar 2022 - 1:33

85

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Construction of flat functions

Published on 16 Mar 2022 - 11:43

93

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differentials of smoothly varying family of maps

Published on 26 Mar 2026 - 12:37

List Question

Determining whether the evaluation mapping $p \mapsto \frac{d}{dx}\bigg|_p$ is smooth

$\psi' \circ F \circ (\varphi')^{-1}$ is $C^\infty$ at $\varphi'(p)$.

Do test functions have smooth extensions?

Is the function $f(x)=\frac{\left(1-x^2+\sqrt{\left(1-x^2\right)^2}\right)}{2}e^{-\frac{x^2}{1-x^2}}$ a bump-function $\in C_c^\infty$? Diff. Eq.?

Generalization of differentiability/smoothness class "$C^n$" notation

Proving that $\lambda$ is not analytic in differential topology.

Smoothness of a function after integration w.r.t. one variable

Regarding Theorem 1.9, Conway, complex Analysis

What is the domain of $g^* \circ f^*$?

For a Lie-group G and embedded Lie-subgroups K < H < G, prove that $\pi:G/K \rightarrow G/H$ is a surjective smooth submersion

Mathematical Definition of "Smoothness" : Requirement of Differentiable Functions to be Smooth?

Smooth Atlas of a Smooth Manifold

How to prove product and quotient of smooth functions is smooth

Construction of flat functions

differentials of smoothly varying family of maps

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