Question

Quotient space of a linear space space is also linear?

score 53 · Answer 1 · 2026-04-14 11:15:40

53

Views

Quotient space of a linear space space is also linear?

Published on 14 Apr 2026 - 11:15

score 588 · Answer 2 · 2026-04-11 15:49:51

588

Views

Tangent Space Well Defined?

Published on 11 Apr 2026 - 15:49

score 167 · Answer 3 · 2026-04-13 09:25:24

167

Views

Orient Manifold

Published on 13 Apr 2026 - 9:25

score 1.4k · Answer 4 · 2026-04-14 12:22:44

1.4k

Views

Jacobian of a diffeomorphism

Published on 14 Apr 2026 - 12:22

score 90 · Answer 5 · 2026-04-09 19:10:17

90

Views

Extending covering projection of the boundary

Published on 09 Apr 2026 - 19:10

score 183 · Answer 6 · 2026-04-12 07:52:05

183

Views

Embedded submanifolds

Published on 12 Apr 2026 - 7:52

score 85 · Answer 7 · 2026-04-16 16:41:48

85

Views

What's the surface measure (volume) of the manifold $x_1^2 + x_2^2 = x_3^2 + x_4^2$, $0 \leq x_1^2 + x_2^2 \leq a^2$?

Published on 16 Apr 2026 - 16:41

score 141 · Answer 8 · 2026-04-12 01:56:17

141

Views

Is $\mathbb{R}\times\{0,1\}$ a manifold?

Published on 12 Apr 2026 - 1:56

score 620 · Answer 9 · 2026-04-14 14:43:05

620

Views

Is the restriction of a smooth vector field to a regular submanifold also smooth?

Published on 14 Apr 2026 - 14:43

score 81 · Answer 10 · 2026-03-27 06:34:56

81

Views

How to define an atlas on this manifold with boundary?

Published on 27 Mar 2026 - 6:34

score 56 · Answer 11 · 2026-04-14 05:33:26

56

Views

What do we need to guarantee that $[X, Y]_p$ is linearly independent with $X_p$ and $Y_p$?

Published on 14 Apr 2026 - 5:33

score 103 · Answer 12 · 2026-03-29 17:25:22

103

Views

M is a k-manifold if and only if $\phi(M)$ is a k-manifold

Published on 29 Mar 2026 - 17:25

score 41 · Answer 13 · 2026-04-15 18:14:38

41

Views

It can happen that $M_1 \cap M_2 =\emptyset $ but $M_1 \cup M_2$ is not a $k$-dimensional manifold. Give a counter example.

Published on 15 Apr 2026 - 18:14

score 135 · Answer 14 · 2026-04-14 03:57:03

135

Views

calculate the surface of the manifold in $\Bbb{R}^4$

Published on 14 Apr 2026 - 3:57

score 605 · Answer 15 · 2026-04-12 05:19:54

What are the "technical troubles" with using a metric space rather than a topological space when defining an abstract manifold? (As in Spivak)

List Question

Quotient space of a linear space space is also linear?

Tangent Space Well Defined?

Orient Manifold

Jacobian of a diffeomorphism

Extending covering projection of the boundary

Embedded submanifolds

What's the surface measure (volume) of the manifold $x_1^2 + x_2^2 = x_3^2 + x_4^2$, $0 \leq x_1^2 + x_2^2 \leq a^2$?

Is $\mathbb{R}\times\{0,1\}$ a manifold?

Is the restriction of a smooth vector field to a regular submanifold also smooth?

How to define an atlas on this manifold with boundary?

What do we need to guarantee that $[X, Y]_p$ is linearly independent with $X_p$ and $Y_p$?

M is a k-manifold if and only if $\phi(M)$ is a k-manifold

It can happen that $M_1 \cap M_2 =\emptyset $ but $M_1 \cup M_2$ is not a $k$-dimensional manifold. Give a counter example.

calculate the surface of the manifold in $\Bbb{R}^4$

What are the "technical troubles" with using a metric space rather than a topological space when defining an abstract manifold? (As in Spivak)

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