Question

Is there a good reason why continuity assumed in the definition of differentiability in do Carmo?

score 87 · Answer 1 · 2026-04-09 10:31:16

87

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Is there a good reason why continuity assumed in the definition of differentiability in do Carmo?

Published on 09 Apr 2026 - 10:31

score 93 · Answer 2 · 2023-10-01 16:00:53

93

Views

The space of all square matrices with the same distinct real eigenvalues is a smooth submanifold of $\mathrm{Mat}(n,\mathbb{R})$

Published on 01 Oct 2023 - 16:00

score 225 · Answer 3 · 2026-03-28 17:25:54

225

Views

Standard area form on a Riemannian manifold.

Published on 28 Mar 2026 - 17:25

score 36 · Answer 4 · 2023-10-03 11:12:50

36

Views

A domain with odd-dimensional boundary

Published on 03 Oct 2023 - 11:12

score 81 · Answer 5 · 2026-04-11 21:05:21

81

Views

How do I prove these facts regarding the proof of a lemma related to partitions of unity regarding local finiteness of a collection?

Published on 11 Apr 2026 - 21:05

score 37 · Answer 6 · 2026-04-12 00:47:34

37

Views

Applications and Interpretation of Jacobian in Square-to-Torus and Square-to-Sphere Transformations

Published on 12 Apr 2026 - 0:47

score 62 · Answer 7 · 2026-03-25 18:45:22

62

Views

Frankel exercise on coordinate invariant vector fields on $TM$

Published on 25 Mar 2026 - 18:45

score 58 · Answer 8 · 2026-03-30 16:06:03

58

Views

Is every properly embeded codimension 1 submanifold of a preimage of a regular value on $S^1$?

Published on 30 Mar 2026 - 16:06

score 39 · Answer 9 · 2026-04-10 19:45:15

39

Views

About the smoothness of a map

Published on 10 Apr 2026 - 19:45

score 44 · Answer 10 · 2023-10-09 14:36:02

44

Views

Degree mod 2 of composition is product of degree mod 2

Published on 09 Oct 2023 - 14:36

score 58 · Answer 11 · 2026-03-26 04:51:43

58

Views

Function on "figure eight" which is not a diffeomorphism due to its topology

Published on 26 Mar 2026 - 4:51

score 43 · Answer 12 · 2026-03-26 16:06:55

43

Views

Lie derivative of one-forms

Published on 26 Mar 2026 - 16:06

score 49 · Answer 13 · 2026-04-11 09:23:03

49

Views

Equivalences of different perspectives of a connection on a principal bundle

Published on 11 Apr 2026 - 9:23

score 54 · Answer 14 · 2026-03-25 12:50:12

54

Views

When is a ray transversal to a hypersurface? Stuck on a step in a proof of the Jordan-Brouwer separation theorem

Published on 25 Mar 2026 - 12:50

score 35 · Answer 15 · 2026-03-26 06:17:20

35

Views

embedding continuous function as diffeomorphism

Published on 26 Mar 2026 - 6:17

List Question

Is there a good reason why continuity assumed in the definition of differentiability in do Carmo?

The space of all square matrices with the same distinct real eigenvalues is a smooth submanifold of $\mathrm{Mat}(n,\mathbb{R})$

Standard area form on a Riemannian manifold.

A domain with odd-dimensional boundary

How do I prove these facts regarding the proof of a lemma related to partitions of unity regarding local finiteness of a collection?

Applications and Interpretation of Jacobian in Square-to-Torus and Square-to-Sphere Transformations

Frankel exercise on coordinate invariant vector fields on $TM$

Is every properly embeded codimension 1 submanifold of a preimage of a regular value on $S^1$?

About the smoothness of a map

Degree mod 2 of composition is product of degree mod 2

Function on "figure eight" which is not a diffeomorphism due to its topology

Lie derivative of one-forms

Equivalences of different perspectives of a connection on a principal bundle

When is a ray transversal to a hypersurface? Stuck on a step in a proof of the Jordan-Brouwer separation theorem

embedding continuous function as diffeomorphism

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