List questions from smooth-functions

Published on 25 Mar 2026 - 4:42

222

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Smooth but not convex

Published on 25 Mar 2026 - 15:38

196

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smoothness of a map that comes from a smooth submersion

Published on 17 Sep 2018 - 6:38

116

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Is it possible $\cos \phi (s)$ and $\sin \phi (s)$ to be nth order differentiable and not $\phi (s)$?

Published on 19 Sep 2018 - 1:30

185

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Confused by conditions for smoothness for a complex curve. Tangent exists vs smoothness

Published on 20 Sep 2018 - 22:21

316

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Inverse function theorem: derive stronger form

Published on 22 Sep 2018 - 20:24

766

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Show that inversion is a smooth operator

Published on 23 Sep 2018 - 8:47

371

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Show that rational function of $C^k$ polynomials is $C^k$

Published on 23 Sep 2018 - 9:52

119

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Derivations and the tangent space on $\mathbb{S}^2$

Published on 24 Sep 2018 - 1:07

300

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if $d_f \neq 0$ then f is a submersion

Published on 24 Sep 2018 - 17:57

1.6k

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Differential of a smooth map over a manifold

Published on 25 Sep 2018 - 16:59

363

Views

Choosing Coordinate Charts -- Smooth Functions on Manifolds

Published on 27 Sep 2018 - 4:54

149

Views

Existence of a smooth extension vanishes at infinity

Published on 25 Mar 2026 - 18:56

392

Views

C^infty approximation of Heaviside step function: definite integral of a bump function

Published on 25 Mar 2026 - 18:53

1k

Views

Existence of a smooth map from the Circle to the Square

Published on 25 Mar 2026 - 4:40

List Question

If a composition of functions is smooth and one of them is smooth, then the other is smooth

Smooth but not convex

smoothness of a map that comes from a smooth submersion

Is it possible $\cos \phi (s)$ and $\sin \phi (s)$ to be nth order differentiable and not $\phi (s)$?

Confused by conditions for smoothness for a complex curve. Tangent exists vs smoothness

Inverse function theorem: derive stronger form

Show that inversion is a smooth operator

Show that rational function of $C^k$ polynomials is $C^k$

Derivations and the tangent space on $\mathbb{S}^2$

if $d_f \neq 0$ then f is a submersion

Differential of a smooth map over a manifold

Choosing Coordinate Charts -- Smooth Functions on Manifolds

Existence of a smooth extension vanishes at infinity

C^infty approximation of Heaviside step function: definite integral of a bump function

Existence of a smooth map from the Circle to the Square

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