List questions from smooth-functions

Published on 25 Mar 2026 - 7:48

59

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How to prove $\mathbb R/(\mathbb Z+\alpha \mathbb Z) \simeq \mathbb T^2/\Delta_\alpha$, the irrational torus, in diffeology?

Published on 25 Mar 2026 - 14:07

34

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extension of a function in n-dimension preserving smoothness

Published on 06 Mar 2020 - 8:53

58

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Is the function $f(x) = e^{||x||^2_2}$ smooth (infinitely differentiable)?

Published on 06 Mar 2020 - 10:18

132

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Are radially symmetric maps smooth at the origin?

Published on 26 Mar 2026 - 23:09

118

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Why is the function $y(x) = \frac{1}{x}$ not a distribution?

Published on 25 Mar 2026 - 11:12

32

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definition of convergence in distributions

Published on 09 Mar 2020 - 16:48

100

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What is a delta family?

Published on 09 Mar 2020 - 17:47

70

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Domain of Test Function

Published on 26 Mar 2026 - 22:19

88

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Can $\psi(x)\cos(\phi(x)),\,\, f_2(x)=\psi(x)\sin(\phi(x))$ be $C^{\infty}$ at zero when $\phi'$ explodes?

Published on 26 Mar 2026 - 14:42

260

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Question in Lee's Introduction to Smooth Manifolds, Corollary 6.17

Published on 24 Mar 2020 - 5:44

332

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Piecewise analytic function

Published on 25 Mar 2026 - 11:25

236

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Show that a constant function does not lie in $W_0^{1,1}((-1,1))$

Published on 26 Mar 2026 - 14:19

648

Views

$n$th order Taylor polynomial formula varies with the inner product?

Published on 31 Mar 2020 - 14:47

59

Views

Munkres Analysis on Manifolds: Proving a function is smooth.

Published on 02 Apr 2020 - 1:01

List Question

Abelian covers of smooth algebraic varieties

How to prove $\mathbb R/(\mathbb Z+\alpha \mathbb Z) \simeq \mathbb T^2/\Delta_\alpha$, the irrational torus, in diffeology?

extension of a function in n-dimension preserving smoothness

Is the function $f(x) = e^{||x||^2_2}$ smooth (infinitely differentiable)?

Are radially symmetric maps smooth at the origin?

Why is the function $y(x) = \frac{1}{x}$ not a distribution?

definition of convergence in distributions

What is a delta family?

Domain of Test Function

Can $\psi(x)\cos(\phi(x)),\,\, f_2(x)=\psi(x)\sin(\phi(x))$ be $C^{\infty}$ at zero when $\phi'$ explodes?

Question in Lee's Introduction to Smooth Manifolds, Corollary 6.17

Piecewise analytic function

Show that a constant function does not lie in $W_0^{1,1}((-1,1))$

$n$th order Taylor polynomial formula varies with the inner product?

Munkres Analysis on Manifolds: Proving a function is smooth.

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