Question

Does the fixed point in the Brouwer's Fixed-Point Theorem have to be an interior point?

score 689 · Answer 1 · 2026-04-17 02:44:59

689

Views

Does the fixed point in the Brouwer's Fixed-Point Theorem have to be an interior point?

Published on 17 Apr 2026 - 2:44

score 3.3k · Answer 2 · 2026-04-25 12:10:43

3.3k

Views

A compact, connected, abelian Lie group is a torus?

Published on 25 Apr 2026 - 12:10

score 222 · Answer 3 · 2026-04-15 12:58:13

222

Views

$N$ commuting vector fields on an $N$-dimensional compact manifold

Published on 15 Apr 2026 - 12:58

score 354 · Answer 4 · 2026-04-16 15:31:28

$X$ is connected and $\mathcal{U}$ is a locally finite collection of precompact open sets that covers $X$; then $\mathcal{U}$ has a countable subcover

score 358 · Answer 5 · 2026-04-13 12:55:03

358

Views

"Error"/"Gap" in proof on every topological manifold being regular

Published on 13 Apr 2026 - 12:55

score 126 · Answer 6 · 2026-04-10 17:22:54

126

Views

Open balls in the definition of a Euclidean submanifold

Published on 10 Apr 2026 - 17:22

score 54 · Answer 7 · 2026-04-14 07:35:05

54

Views

A function $f: \Bbb R \to \Bbb R$ which is differentiable at a point but not $C^1$ at that point.

Published on 14 Apr 2026 - 7:35

score 102 · Answer 8 · 2026-04-16 02:48:23

102

Views

Closed orientable three manifold with finite cover by $S^1 \times S^2$ or $T^3$

Published on 16 Apr 2026 - 2:48

score 109 · Answer 9 · 2026-04-10 12:18:26

109

Views

Derivation of tensor components transformation in tangent space

Published on 10 Apr 2026 - 12:18

score 85 · Answer 10 · 2026-04-15 13:47:40

85

Views

Is the signature of inverse images of diffeomorphic submanifolds (along a homotopy equivalence) the same?

Published on 15 Apr 2026 - 13:47

score 207 · Answer 11 · 2026-04-24 15:20:45

207

Views

"Winding number", Chern character and relative signatures of the metric

Published on 24 Apr 2026 - 15:20

score 143 · Answer 12 · 2026-04-13 18:03:04

143

Views

A detail in the proof orientable manifold admits exactly two orientations

Published on 13 Apr 2026 - 18:03

score 81 · Answer 13 · 2026-04-15 19:47:02

81

Views

Proof that a function $f:\mathbb{R}\times\mathbb{R}\to N$ restricts to a smooth function on $S^1$

Published on 15 Apr 2026 - 19:47

score 226 · Answer 14 · 2026-04-15 07:49:58

226

Views

Formal adjoint of curvature (Yang Mills)

Published on 15 Apr 2026 - 7:49

score 121 · Answer 15 · 2026-04-13 04:50:21

121

Views

Do two embeddings of a Euclidean space into a higher dimensional one only differ by a diffeomorphism?

Published on 13 Apr 2026 - 4:50

List Question

Does the fixed point in the Brouwer's Fixed-Point Theorem have to be an interior point?

A compact, connected, abelian Lie group is a torus?

$N$ commuting vector fields on an $N$-dimensional compact manifold

$X$ is connected and $\mathcal{U}$ is a locally finite collection of precompact open sets that covers $X$; then $\mathcal{U}$ has a countable subcover

"Error"/"Gap" in proof on every topological manifold being regular

Open balls in the definition of a Euclidean submanifold

A function $f: \Bbb R \to \Bbb R$ which is differentiable at a point but not $C^1$ at that point.

Closed orientable three manifold with finite cover by $S^1 \times S^2$ or $T^3$

Derivation of tensor components transformation in tangent space

Is the signature of inverse images of diffeomorphic submanifolds (along a homotopy equivalence) the same?

"Winding number", Chern character and relative signatures of the metric

A detail in the proof orientable manifold admits exactly two orientations

Proof that a function $f:\mathbb{R}\times\mathbb{R}\to N$ restricts to a smooth function on $S^1$

Formal adjoint of curvature (Yang Mills)

Do two embeddings of a Euclidean space into a higher dimensional one only differ by a diffeomorphism?

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