Question

$\mathbb C^2_{0} = \{(a,b)\in X: a\ne 0, b\ne 0\}$ is an open path-connected subset of $\mathbb C^2$

score 227 · Answer 1 · 2021-08-27 11:21:19

227

Views

$\mathbb C^2_{0} = \{(a,b)\in X: a\ne 0, b\ne 0\}$ is an open path-connected subset of $\mathbb C^2$

Published on 27 Aug 2021 - 11:21

score 118 · Answer 2 · 2026-03-28 10:41:35

118

Views

Product of path connected components is isomorphic to path connected components of the product

Published on 28 Mar 2026 - 10:41

score 62 · Answer 3 · 2026-03-29 03:35:34

62

Views

Path-connectedness of a finite cell complex involving a wedge sum of circles

Published on 29 Mar 2026 - 3:35

score 119 · Answer 4 · 2021-09-20 17:08:09

119

Views

In infinite dimensional vector spaces the complementary of a compact is connected

Published on 20 Sep 2021 - 17:08

score 153 · Answer 5 · 2021-09-30 11:10:06

153

Views

Hausdorff dimension of a connected set in $\mathbb{R}^d$

Published on 30 Sep 2021 - 11:10

score 159 · Answer 6 · 2021-09-30 16:47:06

159

Views

Hyperboloid Is (Path) Connected

Published on 30 Sep 2021 - 16:47

score 67 · Answer 7 · 2021-10-03 02:26:18

67

Views

how to prove that a subset is Path-connected

Published on 03 Oct 2021 - 2:26

score 50 · Answer 8 · 2026-02-23 08:42:04

50

Views

Proving/disproving a claim on the relationship between the kinds of connectedness (the usual, and path and local)

Published on 23 Feb 2026 - 8:42

score 38 · Answer 9 · 2021-10-13 22:25:29

38

Views

topological subspace $N_n (S (10))$

Published on 13 Oct 2021 - 22:25

score 37 · Answer 10 · 2021-10-19 06:06:51

37

Views

Show that a subset $X_j$ of the unit circle with $j$ distinct points removed, has exactly $j$ path components ($j \geq 1$)

Published on 19 Oct 2021 - 6:06

score 73 · Answer 11 · 2021-10-19 13:28:24

73

Views

Path connected component

Published on 19 Oct 2021 - 13:28

score 81 · Answer 12 · 2021-10-20 03:22:41

81

Views

Provide an example where $S$ is not path connected, $f:S\longrightarrow T$ is continuous and Im$f$ is path connected.

Published on 20 Oct 2021 - 3:22

score 251 · Answer 13 · 2021-10-26 18:48:09

251

Views

Number of components of a disjoint union of spaces

Published on 26 Oct 2021 - 18:48

score 55 · Answer 14 · 2021-10-28 02:05:00

55

Views

Prove $S^1$ and $\{(x,y) : 1 < x^2+y^2 < 4 \}$ are not homeomorphic using topological invariance of path components.

Published on 28 Oct 2021 - 2:05

score 116 · Answer 15 · 2021-10-28 07:17:18

116

Views

Connectedness of graph of f

Published on 28 Oct 2021 - 7:17

List Question

$\mathbb C^2_{0} = \{(a,b)\in X: a\ne 0, b\ne 0\}$ is an open path-connected subset of $\mathbb C^2$

Product of path connected components is isomorphic to path connected components of the product

Path-connectedness of a finite cell complex involving a wedge sum of circles

In infinite dimensional vector spaces the complementary of a compact is connected

Hausdorff dimension of a connected set in $\mathbb{R}^d$

Hyperboloid Is (Path) Connected

how to prove that a subset is Path-connected

Proving/disproving a claim on the relationship between the kinds of connectedness (the usual, and path and local)

topological subspace $N_n (S (10))$

Show that a subset $X_j$ of the unit circle with $j$ distinct points removed, has exactly $j$ path components ($j \geq 1$)

Path connected component

Provide an example where $S$ is not path connected, $f:S\longrightarrow T$ is continuous and Im$f$ is path connected.

Number of components of a disjoint union of spaces

Prove $S^1$ and $\{(x,y) : 1 < x^2+y^2 < 4 \}$ are not homeomorphic using topological invariance of path components.

Connectedness of graph of f

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