Question

Proof verification: An open connected subset of $\mathbb R^2$ is path connected.

score 154 · Answer 1 · 2019-11-16 02:23:19

154

Views

Proof verification: An open connected subset of $\mathbb R^2$ is path connected.

Published on 16 Nov 2019 - 2:23

score 53 · Answer 2 · 2019-11-17 10:26:58

53

Views

Connected space comprised of disconnected spaces.

Published on 17 Nov 2019 - 10:26

score 485 · Answer 3 · 2019-11-24 15:22:58

485

Views

Strong deformation retract of a singleton implies locally path connected at that point?

Published on 24 Nov 2019 - 15:22

score 230 · Answer 4 · 2019-11-27 22:04:25

230

Views

Question about proof in Van Kampen's theorem; Hatcher

Published on 27 Nov 2019 - 22:04

score 249 · Answer 5 · 2019-11-28 00:15:54

249

Views

Must a neighbourhood of a cut point $x$ of a topological space $X$ contain points from all path-components of $X\setminus\{x\}$?

Published on 28 Nov 2019 - 0:15

score 557 · Answer 6 · 2026-03-25 12:52:49

557

Views

A question regarding a $k$-connected graph

Published on 25 Mar 2026 - 12:52

score 1.1k · Answer 7 · 2019-12-16 07:23:05

1.1k

Views

Path components of Topologist's Sine Curve

Published on 16 Dec 2019 - 7:23

score 157 · Answer 8 · 2019-12-28 02:55:18

157

Views

Path-connected symmetric product $\frac{X^n}{S_n}$ implies path-connected space X?

Published on 28 Dec 2019 - 2:55

score 289 · Answer 9 · 2020-01-03 23:41:26

289

Views

Proposition 1.16 in Lee's Introduction to Smooth Manifolds

Published on 03 Jan 2020 - 23:41

score 36 · Answer 10 · 2020-01-16 18:53:02

36

Views

Finding all covering spaces of the orbit space $Z$ of an action $\Bbb Z_2 \times S^m \times S^n \to S^m \times S^n$

Published on 16 Jan 2020 - 18:53

score 34 · Answer 11 · 2020-01-20 11:29:17

34

Views

$X=\{(x,y)\mid x = r\cos(\frac{\pi}{2^n}), y = r\sin(\frac{\pi}{2^n}), 0\leq r\leq1, n = 2,3,4, \ldots\}$ $\cup \{(0,1)\}$ with the usual topology.

Published on 20 Jan 2020 - 11:29

score 66 · Answer 12 · 2020-01-28 02:36:34

66

Views

$X$ path connected space simple connected if only if map $S^1 \rightarrow X$ extends to $D^2 \rightarrow X$

Published on 28 Jan 2020 - 2:36

score 150 · Answer 13 · 2026-03-25 12:49:58

150

Views

Convex hull of path in $\mathbb R^2$ is the set of convex combination of 2 points of the path

Published on 25 Mar 2026 - 12:49

score 155 · Answer 14 · 2020-02-12 15:00:45

155

Views

Connected Component of Identity of Lie Group is Path Connected

Published on 12 Feb 2020 - 15:00

score 737 · Answer 15 · 2026-02-23 01:02:40

737

Views

Where is a non-empty open set connected iff path-connected?

Published on 23 Feb 2026 - 1:02

List Question

Proof verification: An open connected subset of $\mathbb R^2$ is path connected.

Connected space comprised of disconnected spaces.

Strong deformation retract of a singleton implies locally path connected at that point?

Question about proof in Van Kampen's theorem; Hatcher

Must a neighbourhood of a cut point $x$ of a topological space $X$ contain points from all path-components of $X\setminus\{x\}$?

A question regarding a $k$-connected graph

Path components of Topologist's Sine Curve

Path-connected symmetric product $\frac{X^n}{S_n}$ implies path-connected space X?

Proposition 1.16 in Lee's Introduction to Smooth Manifolds

Finding all covering spaces of the orbit space $Z$ of an action $\Bbb Z_2 \times S^m \times S^n \to S^m \times S^n$

$X=\{(x,y)\mid x = r\cos(\frac{\pi}{2^n}), y = r\sin(\frac{\pi}{2^n}), 0\leq r\leq1, n = 2,3,4, \ldots\}$ $\cup \{(0,1)\}$ with the usual topology.

$X$ path connected space simple connected if only if map $S^1 \rightarrow X$ extends to $D^2 \rightarrow X$

Convex hull of path in $\mathbb R^2$ is the set of convex combination of 2 points of the path

Connected Component of Identity of Lie Group is Path Connected

Where is a non-empty open set connected iff path-connected?

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