Question

Reduced homology group $H_k(S^4 - N^4, \mathbb Z)=H^{4-k}(S^4 - N^4,\mathbb Z)=H_{k-1}(N^4, \mathbb Z)=\mathbb Z^2$?

score 85 · Answer 1 · 2026-05-10 14:32:18

85

Views

Reduced homology group $H_k(S^4 - N^4, \mathbb Z)=H^{4-k}(S^4 - N^4,\mathbb Z)=H_{k-1}(N^4, \mathbb Z)=\mathbb Z^2$?

Published on 10 May 2026 - 14:32

score 253 · Answer 2 · 2026-05-10 15:13:10

253

Views

Topological space formed by the identification of a unit square

Published on 10 May 2026 - 15:13

score 48 · Answer 3 · 2026-04-14 14:39:23

48

Views

Is every finite, nondiscrete $T_0$ space connected?

Published on 14 Apr 2026 - 14:39

score 51 · Answer 4 · 2026-04-14 08:51:16

51

Views

The intersection of infinitely many open sets is closed (Proof for specific example)

Published on 14 Apr 2026 - 8:51

score 104 · Answer 5 · 2026-04-11 15:08:19

104

Views

What does "topological heuristics" refer to here?

Published on 11 Apr 2026 - 15:08

score 501 · Answer 6 · 2026-05-11 00:43:08

501

Views

Prime Integer Topology is $T_2$ but not $T_3$

Published on 11 May 2026 - 0:43

score 63 · Answer 7 · 2026-04-15 20:36:40

63

Views

Consider $\{(−1)^n + 1/n : n \in \Bbb N\setminus \{0\}\}\subset \Bbb R$. Is this set open or closed?

Published on 15 Apr 2026 - 20:36

score 26 · Answer 8 · 2026-04-13 14:02:29

26

Views

A characteristic continuous mapping

Published on 13 Apr 2026 - 14:02

score 62 · Answer 9 · 2026-04-29 06:30:35

62

Views

$[0,1]$ is compact regarding the basis $\mathscr{B}=\{\{q\}:q\in\mathbb{Q}\cap[0,1]\}\cup\{]a,b[:0\leqslant a<b\leqslant 1\}\}$

Published on 29 Apr 2026 - 6:30

score 266 · Answer 10 · 2026-04-15 22:48:42

266

Views

Connectedness of complements of vector subspaces of $\mathbb{R}^n$

Published on 15 Apr 2026 - 22:48

score 188 · Answer 11 · 2026-05-10 21:58:43

188

Views

Extended mapping class group of $S^p \times S^q$

Published on 10 May 2026 - 21:58

score 1.1k · Answer 12 · 2026-04-15 18:23:35

1.1k

Views

Determine which of the following collections of subsets of $\mathbb{R}$ are bases

Published on 15 Apr 2026 - 18:23

score 268 · Answer 13 · 2026-04-11 03:32:15

268

Views

On the spectrum of a self-adjoint operator

Published on 11 Apr 2026 - 3:32

score 4k · Answer 14 · 2026-04-13 15:22:36

4k

Views

Why aren’t continuous functions defined the other way around?

Published on 13 Apr 2026 - 15:22

score 753 · Answer 15 · 2026-05-10 16:32:54

753

Views

Literature on relationship between strong and weak* (weak star) convergence

Published on 10 May 2026 - 16:32

List Question

Reduced homology group $H_k(S^4 - N^4, \mathbb Z)=H^{4-k}(S^4 - N^4,\mathbb Z)=H_{k-1}(N^4, \mathbb Z)=\mathbb Z^2$?

Topological space formed by the identification of a unit square

Is every finite, nondiscrete $T_0$ space connected?

The intersection of infinitely many open sets is closed (Proof for specific example)

What does "topological heuristics" refer to here?

Prime Integer Topology is $T_2$ but not $T_3$

Consider $\{(−1)^n + 1/n : n \in \Bbb N\setminus \{0\}\}\subset \Bbb R$. Is this set open or closed?

A characteristic continuous mapping

$[0,1]$ is compact regarding the basis $\mathscr{B}=\{\{q\}:q\in\mathbb{Q}\cap[0,1]\}\cup\{]a,b[:0\leqslant a<b\leqslant 1\}\}$

Connectedness of complements of vector subspaces of $\mathbb{R}^n$

Extended mapping class group of $S^p \times S^q$

Determine which of the following collections of subsets of $\mathbb{R}$ are bases

On the spectrum of a self-adjoint operator

Why aren’t continuous functions defined the other way around?

Literature on relationship between strong and weak* (weak star) convergence

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