Question

Open sets in quotient space defined by equivalence relation

score 201 · Answer 1 · 2026-04-11 00:54:03

201

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Open sets in quotient space defined by equivalence relation

Published on 11 Apr 2026 - 0:54

score 2k · Answer 2 · 2026-04-18 22:32:15

2k

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Proving the identity functions is continuous iff $\tau_1\supseteq\tau_2$

Published on 18 Apr 2026 - 22:32

score 1.1k · Answer 3 · 2026-04-16 10:57:46

Is $\{ (e^{2\pi i a n},e^{2\pi i b n }) : n \in \mathbb{Z} \}$ dense in the torus, where $a,b$ irrationals such that $a/b$ irrational?

score 1.1k · Answer 4 · 2026-04-14 12:15:42

1.1k

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Proving a space is Hausdorff if $f$ is continuous and bijective

Published on 14 Apr 2026 - 12:15

score 129 · Answer 5 · 2026-04-12 11:54:43

129

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Basis of topological space and topological subspace

Published on 12 Apr 2026 - 11:54

score 91 · Answer 6 · 2026-04-15 19:37:12

91

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How to show that $\bigcup_{n \in \mathbb{N}} \{ \frac{k}{2^n} : 1 \leq k \leq 2^n \}$ is dense in $\mathbb{Q} \cap [0,1]$?

Published on 15 Apr 2026 - 19:37

score 353 · Answer 7 · 2026-04-29 12:45:56

353

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Klein bottle is homeomorphic to unit square quotient

Published on 29 Apr 2026 - 12:45

score 138 · Answer 8 · 2026-04-12 08:03:56

138

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Baby Rudin ch4 ex6: $f$ is continuous on $E$, which is compact, if and only if its graph is compact.

Published on 12 Apr 2026 - 8:03

score 63 · Answer 9 · 2026-04-12 15:28:31

63

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Help verifying my proof

Published on 12 Apr 2026 - 15:28

score 942 · Answer 10 · 2026-04-11 10:30:13

942

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How to prove (rigorously) that these spaces are homotopy equivalent?

Published on 11 Apr 2026 - 10:30

score 53 · Answer 11 · 2026-04-14 18:21:35

53

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Understanding Order topology on a particular set

Published on 14 Apr 2026 - 18:21

score 329 · Answer 12 · 2026-04-14 11:54:19

329

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In what sense is a constant sheaf of abelian groups with stalks G isomorphic to G?

Published on 14 Apr 2026 - 11:54

score 42 · Answer 13 · 2026-04-15 13:26:40

42

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Why this property of open sets in $\mathbb{R}^1$ cannot be generalized on the large dimensions

Published on 15 Apr 2026 - 13:26

score 373 · Answer 14 · 2026-04-13 20:23:54

373

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Let $f:X \to Y$ be a map between two topological spaces. Prove that the following statements are equivalent.

Published on 13 Apr 2026 - 20:23

score 124 · Answer 15 · 2026-04-11 15:25:56

124

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A nice conjecture about convexity

Published on 11 Apr 2026 - 15:25

List Question

Open sets in quotient space defined by equivalence relation

Proving the identity functions is continuous iff $\tau_1\supseteq\tau_2$

Is $\{ (e^{2\pi i a n},e^{2\pi i b n }) : n \in \mathbb{Z} \}$ dense in the torus, where $a,b$ irrationals such that $a/b$ irrational?

Proving a space is Hausdorff if $f$ is continuous and bijective

Basis of topological space and topological subspace

How to show that $\bigcup_{n \in \mathbb{N}} \{ \frac{k}{2^n} : 1 \leq k \leq 2^n \}$ is dense in $\mathbb{Q} \cap [0,1]$?

Klein bottle is homeomorphic to unit square quotient

Baby Rudin ch4 ex6: $f$ is continuous on $E$, which is compact, if and only if its graph is compact.

Help verifying my proof

How to prove (rigorously) that these spaces are homotopy equivalent?

Understanding Order topology on a particular set

In what sense is a constant sheaf of abelian groups with stalks G isomorphic to G?

Why this property of open sets in $\mathbb{R}^1$ cannot be generalized on the large dimensions

Let $f:X \to Y$ be a map between two topological spaces. Prove that the following statements are equivalent.

A nice conjecture about convexity

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