Question

Path-connectedness in the language of category theory?

score 106 · Answer 1 · 2023-04-12 19:30:21

106

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Path-connectedness in the language of category theory?

Published on 12 Apr 2023 - 19:30

score 29 · Answer 2 · 2026-03-27 07:17:14

29

Views

Does there exist $M>0$ such that every $x,y\in U$ can be connected by a path $l$ with $|l|< M|x-y|$ in an open, bounded and path-connect set $U$?

Published on 27 Mar 2026 - 7:17

score 54 · Answer 3 · 2026-03-27 07:15:06

54

Views

Existence of $M>0$ s.t. every $x,y\in K\subset U$ can be connected by a path $l$ s.t. $|l|<M|x-y|$ for compact & connect $K$ and bounded open $U$?

Published on 27 Mar 2026 - 7:15

score 132 · Answer 4 · 2026-03-25 14:21:28

132

Views

Is $\mathbb{R}$ under the countable complement topology path connected? (Proof check)

Published on 25 Mar 2026 - 14:21

score 85 · Answer 5 · 2023-05-09 01:10:33

85

Views

Disconnected boundaries of connected sets in $\mathbb{R}^2$

Published on 09 May 2023 - 1:10

score 67 · Answer 6 · 2023-05-14 03:19:40

67

Views

Chapter 5, Section 5 Exercise 3 is false of James Dugundji Topology

Published on 14 May 2023 - 3:19

score 94 · Answer 7 · 2023-05-18 00:32:45

94

Views

minimal $U$ where $\mathbb R^{\mathbb R} - U$ is not path connected.

Published on 18 May 2023 - 0:32

score 60 · Answer 8 · 2023-05-21 08:18:34

60

Views

Existence of holomorphic Antiderivative of$f(z)=\frac{z^2}{z^2-1}, \quad f: \{z\in \mathbb{C}: |z| >2\} \to \mathbb{C}$

Published on 21 May 2023 - 8:18

score 68 · Answer 9 · 2023-05-21 14:24:48

68

Views

Does $f(z)=\frac{e^z+\sin(z)}{z}$ have a complex antiderivative on $\mathbb{C}/\{0\}$

Published on 21 May 2023 - 14:24

score 36 · Answer 10 · 2023-05-30 21:29:34

36

Views

Connectedness of the adherent values of a sequence

Published on 30 May 2023 - 21:29

score 201 · Answer 11 · 2023-06-09 18:44:55

201

Views

Munkres' proof that topologist's sine curve is not path connected

Published on 09 Jun 2023 - 18:44

score 49 · Answer 12 · 2023-06-09 23:35:30

49

Views

Points of boundary of open path-connected set which don't break path-connectedness

Published on 09 Jun 2023 - 23:35

score 33 · Answer 13 · 2023-06-21 13:46:51

33

Views

Is the hypograph of a bounded function path connected?

Published on 21 Jun 2023 - 13:46

score 131 · Answer 14 · 2023-06-26 08:23:19

131

Views

Metric space arc-connectedness

Published on 26 Jun 2023 - 8:23

score 67 · Answer 15 · 2023-07-04 16:38:48

67

Views

Existence of paths obeying partial ordering

Published on 04 Jul 2023 - 16:38

List Question

Path-connectedness in the language of category theory?

Does there exist $M>0$ such that every $x,y\in U$ can be connected by a path $l$ with $|l|< M|x-y|$ in an open, bounded and path-connect set $U$?

Existence of $M>0$ s.t. every $x,y\in K\subset U$ can be connected by a path $l$ s.t. $|l|<M|x-y|$ for compact & connect $K$ and bounded open $U$?

Is $\mathbb{R}$ under the countable complement topology path connected? (Proof check)

Disconnected boundaries of connected sets in $\mathbb{R}^2$

Chapter 5, Section 5 Exercise 3 is false of James Dugundji Topology

minimal $U$ where $\mathbb R^{\mathbb R} - U$ is not path connected.

Existence of holomorphic Antiderivative of$f(z)=\frac{z^2}{z^2-1}, \quad f: \{z\in \mathbb{C}: |z| >2\} \to \mathbb{C}$

Does $f(z)=\frac{e^z+\sin(z)}{z}$ have a complex antiderivative on $\mathbb{C}/\{0\}$

Connectedness of the adherent values of a sequence

Munkres' proof that topologist's sine curve is not path connected

Points of boundary of open path-connected set which don't break path-connectedness

Is the hypograph of a bounded function path connected?

Metric space arc-connectedness

Existence of paths obeying partial ordering

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