Question

Find if $W=\lbrace z\in \mathbb{C}\mid 2 \leq |z| \leq 3 \rbrace$ set is connected and compact

score 58 · Answer 1 · 2021-02-27 04:56:57

58

Views

Find if $W=\lbrace z\in \mathbb{C}\mid 2 \leq |z| \leq 3 \rbrace$ set is connected and compact

Published on 27 Feb 2021 - 4:56

score 183 · Answer 2 · 2021-03-06 14:12:09

183

Views

Let $U \subset S^n$ open subset of the sphere homeomorphic to $\mathbb{R}^n$ prove that $\mathbb{S}^n \setminus U$ is connected

Published on 06 Mar 2021 - 14:12

score 85 · Answer 3 · 2021-03-13 12:20:44

85

Views

$\mathbb{C} \setminus \{z \in \mathbb{C} \mid \operatorname{Re}(z)=0\}$ is not simply connected.

Published on 13 Mar 2021 - 12:20

score 472 · Answer 4 · 2021-03-13 19:13:15

472

Views

Path-connectedness of $\mathbb{C}\setminus \lbrace z_1, ..., z_n \rbrace$

Published on 13 Mar 2021 - 19:13

score 278 · Answer 5 · 2021-03-16 22:17:20

278

Views

Path-connected subsets of Q

Published on 16 Mar 2021 - 22:17

score 262 · Answer 6 · 2021-03-24 08:20:08

262

Views

Can the notions of "path" and "connectedness" be generalized to discrete spaces?

Published on 24 Mar 2021 - 8:20

score 323 · Answer 7 · 2021-03-24 13:09:08

323

Views

Clarifying Polygonal Paths in Complex Analysis

Published on 24 Mar 2021 - 13:09

score 333 · Answer 8 · 2021-04-03 11:00:03

333

Views

Existence of rectifiable/piecewise $C^1$ curves between two points of an open connected domain in $\mathbb{C}$

Published on 03 Apr 2021 - 11:00

score 1.3k · Answer 9 · 2026-03-26 19:01:46

1.3k

Views

Show that a graph that is connected but not complete has vertices u,v and w such that uv and vw are edges but not uw.

Published on 26 Mar 2026 - 19:01

score 174 · Answer 10 · 2021-04-13 22:27:12

174

Views

$\varphi$ homotopic to constant iff $\psi$ path homotopic to a constant

Published on 13 Apr 2021 - 22:27

score 172 · Answer 11 · 2021-04-14 18:40:31

172

Views

Connecting Points in a Region $\Omega \subset \mathbb{C}$ by a Piecewise Smooth Curve

Published on 14 Apr 2021 - 18:40

score 1k · Answer 12 · 2021-04-16 07:58:33

1k

Views

In which cases connectedness and path connectedness are equivalent?

Published on 16 Apr 2021 - 7:58

score 46 · Answer 13 · 2021-04-18 07:31:53

46

Views

Is a path-connected set always Jordan-path connected?

Published on 18 Apr 2021 - 7:31

score 122 · Answer 14 · 2021-04-18 13:45:17

122

Views

Homotopy of paths is trivial?

Published on 18 Apr 2021 - 13:45

score 316 · Answer 15 · 2021-04-20 14:26:37

316

Views

Are the path connectedness of $X_0$ and $X_1$ necessary in Seifert-van Kampen theorem?

Published on 20 Apr 2021 - 14:26

List Question

Find if $W=\lbrace z\in \mathbb{C}\mid 2 \leq |z| \leq 3 \rbrace$ set is connected and compact

Let $U \subset S^n$ open subset of the sphere homeomorphic to $\mathbb{R}^n$ prove that $\mathbb{S}^n \setminus U$ is connected

$\mathbb{C} \setminus \{z \in \mathbb{C} \mid \operatorname{Re}(z)=0\}$ is not simply connected.

Path-connectedness of $\mathbb{C}\setminus \lbrace z_1, ..., z_n \rbrace$

Path-connected subsets of Q

Can the notions of "path" and "connectedness" be generalized to discrete spaces?

Clarifying Polygonal Paths in Complex Analysis

Existence of rectifiable/piecewise $C^1$ curves between two points of an open connected domain in $\mathbb{C}$

Show that a graph that is connected but not complete has vertices u,v and w such that uv and vw are edges but not uw.

$\varphi$ homotopic to constant iff $\psi$ path homotopic to a constant

Connecting Points in a Region $\Omega \subset \mathbb{C}$ by a Piecewise Smooth Curve

In which cases connectedness and path connectedness are equivalent?

Is a path-connected set always Jordan-path connected?

Homotopy of paths is trivial?

Are the path connectedness of $X_0$ and $X_1$ necessary in Seifert-van Kampen theorem?

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