List questions from manifolds

Published on 15 Apr 2026 - 8:51

497

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Why are are integrals of functions in coordinates on manifolds not invariant under coordinate transformations?

Published on 15 Apr 2026 - 13:17

164

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Prove: The pre-image of a null-set on a manifold in $\mathbb{R}^k$ is a null-set

Published on 13 Apr 2026 - 21:37

702

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Is there a locally compact, locally connected, Hausdorff and second countable space that is "nowhere locally Euclidean"?

Published on 16 Apr 2026 - 22:25

94

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Is $\overline{u^{-1}((-\infty,a))}$ a $C^k$-manifold with boundary for a $C^k$ function $u$?

Published on 27 Mar 2026 - 8:16

168

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How to construct free subgroup of SO(3) using Baire's Theorem?

Published on 12 Apr 2026 - 3:56

2k

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Extension of Vector field along a curve always exists?

Published on 04 Apr 2026 - 13:21

1k

Views

Integration of a $k$-form over chains

Published on 11 Apr 2026 - 6:20

103

Views

Topological boundary as a submanifold

Published on 27 Mar 2026 - 8:16

48

Views

Linearity in quotient space

Published on 10 Apr 2026 - 21:55

61

Views

Whats the surface area of the surface $0 \leq z, (x-1)^2 + y^2 \leq 1$?

Published on 15 Apr 2026 - 18:18

602

Views

Diffeomorphism group of product manifold

Published on 13 Apr 2026 - 19:44

42

Views

$M=M_1\cup M_2$ is not necessarily a manifold, when $M_1\cap M_2=\emptyset$, $M_i$ a manifold

Published on 15 Apr 2026 - 21:33

107

Views

Apparent violation of fundamental theorem of ODEs, how to resolve?

Published on 08 Apr 2026 - 17:08

183

Views

Why does $(X_a,Y_b)(f\circ \mu(a,b)) = X_a(f\circ R_b(a)) + Y_b(f\circ L_a(b))$?

Published on 04 May 2026 - 19:18

List Question

Differential of a map including a manifold

Why are are integrals of functions in coordinates on manifolds not invariant under coordinate transformations?

Prove: The pre-image of a null-set on a manifold in $\mathbb{R}^k$ is a null-set

Is there a locally compact, locally connected, Hausdorff and second countable space that is "nowhere locally Euclidean"?

Is $\overline{u^{-1}((-\infty,a))}$ a $C^k$-manifold with boundary for a $C^k$ function $u$?

How to construct free subgroup of SO(3) using Baire's Theorem?

Extension of Vector field along a curve always exists?

Integration of a $k$-form over chains

Topological boundary as a submanifold

Linearity in quotient space

Whats the surface area of the surface $0 \leq z, (x-1)^2 + y^2 \leq 1$?

Diffeomorphism group of product manifold

$M=M_1\cup M_2$ is not necessarily a manifold, when $M_1\cap M_2=\emptyset$, $M_i$ a manifold

Apparent violation of fundamental theorem of ODEs, how to resolve?

Why does $(X_a,Y_b)(f\circ \mu(a,b)) = X_a(f\circ R_b(a)) + Y_b(f\circ L_a(b))$?

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