Question

Why the order square is not path-connected

score 1.1k · Answer 1 · 2026-05-06 10:00:13

1.1k

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Why the order square is not path-connected

Published on 06 May 2026 - 10:00

score 1.9k · Answer 2 · 2026-05-06 10:02:38

1.9k

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Prove that $\overline S$ is not path connected, where $S=\{x\times \sin(\frac1x):x\in(0,1]\}$

Published on 06 May 2026 - 10:02

score 1.5k · Answer 3 · 2026-05-05 10:21:09

1.5k

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Is the Mandelbrot set path-connected?

Published on 05 May 2026 - 10:21

score 490 · Answer 4 · 2026-05-06 10:00:09

490

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Example of a topological space that is connected, not locally connected and not path connected

Published on 06 May 2026 - 10:00

score 287 · Answer 5 · 2026-05-05 19:06:57

287

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Example of path connected metric space whose hyperspace with Vietoris topology is not path connected?

Published on 05 May 2026 - 19:06

score 184 · Answer 6 · 2026-05-07 19:46:26

184

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Proof explanation to see that subset of $\mathbb{R}^2$ is not path connected.

Published on 07 May 2026 - 19:46

score 339 · Answer 7 · 2026-05-05 03:42:01

339

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Connectedness and path connectedness of a finer topology

Published on 05 May 2026 - 3:42

score 77 · Answer 8 · 2026-05-07 15:40:55

77

Views

Show that for an abelian countable group $G$ there exists a compact path connected subspace $K ⊆ \Bbb R^4$ such that $H_1(K)$ isomorphic to $G$

Published on 07 May 2026 - 15:40

score 85 · Answer 9 · 2026-05-06 10:00:59

85

Views

Is there a better way - space is not path connected

Published on 06 May 2026 - 10:00

score 165 · Answer 10 · 2026-05-06 07:33:17

165

Views

How to construct a path between two points in a general $n-surface$?

Published on 06 May 2026 - 7:33

score 123 · Answer 11 · 2026-05-06 10:01:19

123

Views

Definition of product implies the existence of continuous function?

Published on 06 May 2026 - 10:01

score 76 · Answer 12 · 2026-04-29 12:46:45

76

Views

Why do we need our set to be simple (connected) for a vector field to be gradient?

Published on 29 Apr 2026 - 12:46

score 332 · Answer 13 · 2026-04-29 12:56:03

332

Views

Why is the topological space of reals defined to be path connected?

Published on 29 Apr 2026 - 12:56

score 122 · Answer 14 · 2026-05-07 13:43:41

122

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Menger type of problem - show that there are pairwise disjoint paths

Published on 07 May 2026 - 13:43

score 493 · Answer 15 · 2026-04-29 12:55:45

493

Views

A question from the proof of topologists sine curve being not path connected

Published on 29 Apr 2026 - 12:55

List Question

Why the order square is not path-connected

Prove that $\overline S$ is not path connected, where $S=\{x\times \sin(\frac1x):x\in(0,1]\}$

Is the Mandelbrot set path-connected?

Example of a topological space that is connected, not locally connected and not path connected

Example of path connected metric space whose hyperspace with Vietoris topology is not path connected?

Proof explanation to see that subset of $\mathbb{R}^2$ is not path connected.

Connectedness and path connectedness of a finer topology

Show that for an abelian countable group $G$ there exists a compact path connected subspace $K ⊆ \Bbb R^4$ such that $H_1(K)$ isomorphic to $G$

Is there a better way - space is not path connected

How to construct a path between two points in a general $n-surface$?

Definition of product implies the existence of continuous function?

Why do we need our set to be simple (connected) for a vector field to be gradient?

Why is the topological space of reals defined to be path connected?

Menger type of problem - show that there are pairwise disjoint paths

A question from the proof of topologists sine curve being not path connected

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