Question

Proving $S^1$, the unit circle in $\mathbb{R}^2$, is path-connected

score 520 · Answer 1 · 2021-05-30 00:55:52

520

Views

Proving $S^1$, the unit circle in $\mathbb{R}^2$, is path-connected

Published on 30 May 2021 - 0:55

score 63 · Answer 2 · 2021-05-30 21:24:47

63

Views

Locus $\{(x,y) \mid xy = 0\}$ is path-connected

Published on 30 May 2021 - 21:24

score 129 · Answer 3 · 2021-06-02 16:46:47

129

Views

Path-connectedness of $S^2$ and $X=\mathbb{C}\setminus\{p_1,\ldots,p_n\}$

Published on 02 Jun 2021 - 16:46

score 44 · Answer 4 · 2021-06-02 19:38:06

44

Views

Suppose $\exists p\in X$ s.t. if $U\subseteq X$ is open and $p\in U$ then $U=X$. Show $X$ is path connected.

Published on 02 Jun 2021 - 19:38

score 183 · Answer 5 · 2021-06-03 08:16:25

183

Views

Closure of simply connected set in $\mathbb{C}$ with smooth boundary is path-connected

Published on 03 Jun 2021 - 8:16

score 13 · Answer 6 · 2021-06-04 20:55:58

13

Views

Map-Making Point Connectivity Problem

Published on 04 Jun 2021 - 20:55

score 468 · Answer 7 · 2021-06-13 06:46:59

468

Views

why is deleted infinite broom not path connected

Published on 13 Jun 2021 - 6:46

score 80 · Answer 8 · 2021-06-16 03:40:21

Proof or disprove: If $C\subseteq \mathbb{R}^n$ is path connected, then the interior $C^°$ is also path connected.

score 64 · Answer 9 · 2021-07-16 05:33:36

64

Views

showing whether $S^1 \cup W$ is (path) connected or not.

Published on 16 Jul 2021 - 5:33

score 509 · Answer 10 · 2021-07-24 05:02:49

509

Views

A simply/path-connected set that is not star-shaped

Published on 24 Jul 2021 - 5:02

score 446 · Answer 11 · 2026-02-23 12:02:58

446

Views

What are the path components of $\mathbb{R}_l$?

Published on 23 Feb 2026 - 12:02

score 206 · Answer 12 · 2021-08-08 01:52:44

206

Views

Given any bounded, simply connected, regular open set on the plane, is the boundary always path connected?

Published on 08 Aug 2021 - 1:52

score 174 · Answer 13 · 2021-08-13 18:37:34

174

Views

Proving not path-connected of a connected set

Published on 13 Aug 2021 - 18:37

score 56 · Answer 14 · 2021-08-16 17:24:21

56

Views

Is this “Combesque” Space path connected.

Published on 16 Aug 2021 - 17:24

score 21 · Answer 15 · 2026-03-28 00:29:50

21

Views

On the Connectedness of a Subspace of Product Space

Published on 28 Mar 2026 - 0:29

List Question

Proving $S^1$, the unit circle in $\mathbb{R}^2$, is path-connected

Locus $\{(x,y) \mid xy = 0\}$ is path-connected

Path-connectedness of $S^2$ and $X=\mathbb{C}\setminus\{p_1,\ldots,p_n\}$

Suppose $\exists p\in X$ s.t. if $U\subseteq X$ is open and $p\in U$ then $U=X$. Show $X$ is path connected.

Closure of simply connected set in $\mathbb{C}$ with smooth boundary is path-connected

Map-Making Point Connectivity Problem

why is deleted infinite broom not path connected

Proof or disprove: If $C\subseteq \mathbb{R}^n$ is path connected, then the interior $C^°$ is also path connected.

showing whether $S^1 \cup W$ is (path) connected or not.

A simply/path-connected set that is not star-shaped

What are the path components of $\mathbb{R}_l$?

Given any bounded, simply connected, regular open set on the plane, is the boundary always path connected?

Proving not path-connected of a connected set

Is this “Combesque” Space path connected.

On the Connectedness of a Subspace of Product Space

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