Question

Are these sets Right hand topology-closed/open on the set of Reals

score 235 · Answer 1 · 2026-04-14 05:18:35

235

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Are these sets Right hand topology-closed/open on the set of Reals

Published on 14 Apr 2026 - 5:18

score 59 · Answer 2 · 2026-04-15 02:39:24

59

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Is $M$ homeomorphic to $\mathbb{S}^2\times \mathbb{S}^1$?

Published on 15 Apr 2026 - 2:39

score 101 · Answer 3 · 2026-04-13 23:57:01

101

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How to show that $\sup(A + B) = \sup\{x + y : x \in A, y \in B\} = \sup A + \sup B$ for bounded subsets $A, B$ of $\mathbb{R}$

Published on 13 Apr 2026 - 23:57

score 42 · Answer 4 · 2026-04-10 03:41:09

42

Views

How can we be sure that fundamental notions of Euclidean geometry hold in higher dimensions?

Published on 10 Apr 2026 - 3:41

score 70 · Answer 5 · 2026-04-14 17:55:26

70

Views

Example of discrete subspace on a plane which has a closure of continuum?

Published on 14 Apr 2026 - 17:55

score 582 · Answer 6 · 2026-04-12 07:56:10

582

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What is the fundamental group of the octahedral symmetry group Oh?

Published on 12 Apr 2026 - 7:56

score 281 · Answer 7 · 2026-04-15 11:14:44

281

Views

On proving that $G/\overline{\{e\}}$ is Hausdorff for a topological group $G$.

Published on 15 Apr 2026 - 11:14

score 124 · Answer 8 · 2026-04-12 14:38:34

124

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Codomain of metric in Munkres

Published on 12 Apr 2026 - 14:38

score 1.5k · Answer 9 · 2026-04-11 16:44:47

1.5k

Views

Definition of Disjoint Union Spaces

Published on 11 Apr 2026 - 16:44

score 112 · Answer 10 · 2026-04-16 04:26:12

112

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If $f : M \to N$ is closed, $\forall\, y \in V \subset N$, $\exists\, U \subset N$ such that $f^{-1}(y) \subset f^{-1}(U) \subset V$

Published on 16 Apr 2026 - 4:26

score 2.8k · Answer 11 · 2026-04-17 06:18:07

2.8k

Views

Prove that the set of convergent sequences is closed

Published on 17 Apr 2026 - 6:18

score 85 · Answer 12 · 2026-04-15 09:20:06

Closure of $ \{n\} $ in $\mathbb{Z}_{\geq 2}$, with the topology $U_k=\{n: n\mid k, n\in\mathbb{Z}_{\geq 2} \}$, $k \in \mathbb{Z}_{\geq 2}$

score 228 · Answer 13 · 2026-04-14 09:30:08

228

Views

Bounded Linear Functionals Form A Compact Space

Published on 14 Apr 2026 - 9:30

score 129 · Answer 14 · 2026-04-15 07:31:56

129

Views

Without axiom of choice, can we prove that there are only countably many disjoint intervals in real line.

Published on 15 Apr 2026 - 7:31

score 391 · Answer 15 · 2026-04-09 11:43:29

391

Views

Equicontinuity of set of polynomials

Published on 09 Apr 2026 - 11:43

List Question

Are these sets Right hand topology-closed/open on the set of Reals

Is $M$ homeomorphic to $\mathbb{S}^2\times \mathbb{S}^1$?

How to show that $\sup(A + B) = \sup\{x + y : x \in A, y \in B\} = \sup A + \sup B$ for bounded subsets $A, B$ of $\mathbb{R}$

How can we be sure that fundamental notions of Euclidean geometry hold in higher dimensions?

Example of discrete subspace on a plane which has a closure of continuum?

What is the fundamental group of the octahedral symmetry group Oh?

On proving that $G/\overline{\{e\}}$ is Hausdorff for a topological group $G$.

Codomain of metric in Munkres

Definition of Disjoint Union Spaces

If $f : M \to N$ is closed, $\forall\, y \in V \subset N$, $\exists\, U \subset N$ such that $f^{-1}(y) \subset f^{-1}(U) \subset V$

Prove that the set of convergent sequences is closed

Closure of $ \{n\} $ in $\mathbb{Z}_{\geq 2}$, with the topology $U_k=\{n: n\mid k, n\in\mathbb{Z}_{\geq 2} \}$, $k \in \mathbb{Z}_{\geq 2}$

Bounded Linear Functionals Form A Compact Space

Without axiom of choice, can we prove that there are only countably many disjoint intervals in real line.

Equicontinuity of set of polynomials

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