Question

Let $f: \mathbb C \to \mathbb C$ be a proper smooth map with continuous extension $F : \mathbb C P^1 \to \mathbb C P^1$. Must $F$ be smooth?

score 61 · Answer 1 · 2026-03-25 09:50:11

61

Views

Let $f: \mathbb C \to \mathbb C$ be a proper smooth map with continuous extension $F : \mathbb C P^1 \to \mathbb C P^1$. Must $F$ be smooth?

Published on 25 Mar 2026 - 9:50

score 46 · Answer 2 · 2026-03-26 11:03:37

46

Views

Are all multivariate elementary functions $C^\infty$ on any open ball for which they are defined?

Published on 26 Mar 2026 - 11:03

score 38 · Answer 3 · 2024-01-22 02:31:47

38

Views

Uniform convergence and extending a smooth function

Published on 22 Jan 2024 - 2:31

score 44 · Answer 4 · 2024-01-27 02:33:45

44

Views

If $f\in C^{\infty}(\mathbb{R})$ and $f(0)=0,$ let $g(t)=\frac{f(t)}{t},$ will $g$ be in $C^{\infty}(\mathbb{R})$?

Published on 27 Jan 2024 - 2:33

score 103 · Answer 5 · 2026-03-25 11:00:47

103

Views

How Can I solve this problem on Hopf Map?

Published on 25 Mar 2026 - 11:00

score 90 · Answer 6 · 2024-02-02 21:39:27

90

Views

Can a smooth matrix function $M_{ij}(t)$ change rank?

Published on 02 Feb 2024 - 21:39

score 33 · Answer 7 · 2024-02-05 10:54:48

33

Views

Unambiguous definition of smoothness in the parameterization of a curve

Published on 05 Feb 2024 - 10:54

score 50 · Answer 8 · 2024-02-06 03:05:33

50

Views

Do smooth curves uniquely identify the smooth structure?

Published on 06 Feb 2024 - 3:05

score 53 · Answer 9 · 2024-02-06 05:14:02

53

Views

Multiplying tangent vectors by positive numbers (Gullemin-Pollack 1.8.2)

Published on 06 Feb 2024 - 5:14

score 126 · Answer 10 · 2024-02-07 19:22:39

126

Views

How to compute $\displaystyle\lim_{n\to\infty} \frac1{n+1}\sum_{k=1}^n \left|X+\frac kn\right|-\left|X-\frac kn\right|$?

Published on 07 Feb 2024 - 19:22

score 73 · Answer 11 · 2024-02-08 19:24:16

73

Views

Example of smooth compactly supported function

Published on 08 Feb 2024 - 19:24

score 65 · Answer 12 · 2024-02-09 00:21:24

65

Views

How do we know that there is a smooth function that is constant on two disjoint non-empty compact sets in $\mathbb{R}^n$?

Published on 09 Feb 2024 - 0:21

score 92 · Answer 13 · 2024-02-14 20:01:59

92

Views

Prove that if every smooth function on a subset of a manifold can be extended to a smooth function on the whole manifold, then the subset is closed.

Published on 14 Feb 2024 - 20:01

score 82 · Answer 14 · 2024-02-16 03:20:54

82

Views

I wonder why the author wrote $\phi_i:\mathbb{R}^n\to\mathbb{R}$ instead of $\phi_i:A\to\mathbb{R}$. ("Analysis on Manifolds" by James R. Munkres.)

Published on 16 Feb 2024 - 3:20

score 53 · Answer 15 · 2026-03-28 02:44:57

53

Views

Can the construction of this 2D Curve of Constant Width be adapted to a 3D Surface of Constant Width?

Published on 28 Mar 2026 - 2:44

List Question

Let $f: \mathbb C \to \mathbb C$ be a proper smooth map with continuous extension $F : \mathbb C P^1 \to \mathbb C P^1$. Must $F$ be smooth?

Are all multivariate elementary functions $C^\infty$ on any open ball for which they are defined?

Uniform convergence and extending a smooth function

If $f\in C^{\infty}(\mathbb{R})$ and $f(0)=0,$ let $g(t)=\frac{f(t)}{t},$ will $g$ be in $C^{\infty}(\mathbb{R})$?

How Can I solve this problem on Hopf Map?

Can a smooth matrix function $M_{ij}(t)$ change rank?

Unambiguous definition of smoothness in the parameterization of a curve

Do smooth curves uniquely identify the smooth structure?

Multiplying tangent vectors by positive numbers (Gullemin-Pollack 1.8.2)

How to compute $\displaystyle\lim_{n\to\infty} \frac1{n+1}\sum_{k=1}^n \left|X+\frac kn\right|-\left|X-\frac kn\right|$?

Example of smooth compactly supported function

How do we know that there is a smooth function that is constant on two disjoint non-empty compact sets in $\mathbb{R}^n$?

Prove that if every smooth function on a subset of a manifold can be extended to a smooth function on the whole manifold, then the subset is closed.

I wonder why the author wrote $\phi_i:\mathbb{R}^n\to\mathbb{R}$ instead of $\phi_i:A\to\mathbb{R}$. ("Analysis on Manifolds" by James R. Munkres.)

Can the construction of this 2D Curve of Constant Width be adapted to a 3D Surface of Constant Width?

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