Question

Show that there is a smooth function $\tilde f\colon M \to \Bbb R$, with $\tilde f_M=f$ and $\operatorname{supp}(\tilde f) \subset U$.

score 179 · Answer 1 · 2026-04-16 19:03:20

Show that there is a smooth function $\tilde f\colon M \to \Bbb R$, with $\tilde f_M=f$ and $\operatorname{supp}(\tilde f) \subset U$.

score 43 · Answer 2 · 2026-04-06 07:16:41

43

Views

Let $f\colon \Bbb R^n \to \Bbb R^n$ be the translation, $f(x)=x+a$. Show that $\deg(f)=1$

Published on 06 Apr 2026 - 7:16

score 116 · Answer 3 · 2026-04-29 18:17:31

116

Views

Are there more convenient charts than Riemannian normal coordinate chart?

Published on 29 Apr 2026 - 18:17

score 32 · Answer 4 · 2026-04-14 06:23:51

32

Views

If $M$ a manifold and $p\in M$, why is there a neighborhood V s.t. $V\subset \overline V\subset W$ with $\overline V$ compact?

Published on 14 Apr 2026 - 6:23

score 47 · Answer 5 · 2026-04-13 23:26:55

47

Views

Is there restriction on the cardinailty of manifold?

Published on 13 Apr 2026 - 23:26

score 68 · Answer 6 · 2026-04-11 07:09:32

68

Views

What's "ancient time"?

Published on 11 Apr 2026 - 7:09

score 188 · Answer 7 · 2026-04-29 18:17:03

188

Views

Smooth extension of a tangent vector

Published on 29 Apr 2026 - 18:17

score 1.8k · Answer 8 · 2026-04-15 06:13:07

1.8k

Views

Why $\mathbb S^1\times \mathbb S^1$ is isomorphic to the torus?

Published on 15 Apr 2026 - 6:13

score 176 · Answer 9 · 2026-04-13 03:26:19

176

Views

Classification of manifold of dimension 1

Published on 13 Apr 2026 - 3:26

score 78 · Answer 10 · 2026-04-07 21:56:36

78

Views

The exterior derivate

Published on 07 Apr 2026 - 21:56

score 23 · Answer 11 · 2026-04-13 04:45:47

23

Views

Different between several proposition - Manifold, plate function.

Published on 13 Apr 2026 - 4:45

score 6.4k · Answer 12 · 2026-04-28 17:47:29

6.4k

Views

Are all Lie groups Matrix Lie groups?

Published on 28 Apr 2026 - 17:47

score 199 · Answer 13 · 2026-04-13 14:11:33

199

Views

Is $C[0,1]$ a manifold?

Published on 13 Apr 2026 - 14:11

score 104 · Answer 14 · 2026-04-14 08:21:35

104

Views

Manifold and submanifold, in $S$ a submanifold?

Published on 14 Apr 2026 - 8:21

score 194 · Answer 15 · 2026-04-10 02:11:05

194

Views

Construct circle as a submanifold of $\mathbb R^2$.

Published on 10 Apr 2026 - 2:11

List Question

Show that there is a smooth function $\tilde f\colon M \to \Bbb R$, with $\tilde f_M=f$ and $\operatorname{supp}(\tilde f) \subset U$.

Let $f\colon \Bbb R^n \to \Bbb R^n$ be the translation, $f(x)=x+a$. Show that $\deg(f)=1$

Are there more convenient charts than Riemannian normal coordinate chart?

If $M$ a manifold and $p\in M$, why is there a neighborhood V s.t. $V\subset \overline V\subset W$ with $\overline V$ compact?

Is there restriction on the cardinailty of manifold?

What's "ancient time"?

Smooth extension of a tangent vector

Why $\mathbb S^1\times \mathbb S^1$ is isomorphic to the torus?

Classification of manifold of dimension 1

The exterior derivate

Different between several proposition - Manifold, plate function.

Are all Lie groups Matrix Lie groups?

Is $C[0,1]$ a manifold?

Manifold and submanifold, in $S$ a submanifold?

Construct circle as a submanifold of $\mathbb R^2$.

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