Question

Is connected component of sublevel set of continuous function always path connected?

score 121 · Answer 1 · 2022-01-04 06:23:11

121

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Is connected component of sublevel set of continuous function always path connected?

Published on 04 Jan 2022 - 6:23

score 83 · Answer 2 · 2026-03-28 03:33:09

83

Views

Path connected product topology implies every topology is path connected

Published on 28 Mar 2026 - 3:33

score 178 · Answer 3 · 2022-01-07 18:47:07

178

Views

How to show that this space is not path connected?

Published on 07 Jan 2022 - 18:47

score 75 · Answer 4 · 2026-02-23 08:40:13

75

Views

Locally connected for sub space topology of $\Bbb R^2$

Published on 23 Feb 2026 - 8:40

score 66 · Answer 5 · 2022-01-13 15:22:22

66

Views

Understanding the definition of path connected subspace

Published on 13 Jan 2022 - 15:22

score 74 · Answer 6 · 2022-01-16 14:10:06

74

Views

Is this graph connected or path-connected?

Published on 16 Jan 2022 - 14:10

score 112 · Answer 7 · 2022-01-17 13:11:56

112

Views

Is $\{ (x, y) \in \mathbb{C}^2 : x^2 + y^2 = 1\}$ connected in $\mathbb{C}^2$?

Published on 17 Jan 2022 - 13:11

score 64 · Answer 8 · 2022-01-17 21:49:35

64

Views

Trouble showing a union of sets is connected.

Published on 17 Jan 2022 - 21:49

score 111 · Answer 9 · 2022-01-19 06:44:24

111

Views

Connectedness of Hartogs' Triangle in $\mathbb C^2$

Published on 19 Jan 2022 - 6:44

score 212 · Answer 10 · 2022-01-20 14:05:58

212

Views

show that in $\mathbb{R}^2$ with the cofinite topology, every open set is both connected and path connected.

Published on 20 Jan 2022 - 14:05

score 91 · Answer 11 · 2022-01-20 18:55:19

91

Views

$C = (\{0\} \times [0,1]) \: \cup \: \{ (\frac{1}{n},y), n \in \mathbb{N}, y \in [0,1] \} \:\cup \: ([0,1] \times \{0\})$ is connected?

Published on 20 Jan 2022 - 18:55

score 32 · Answer 12 · 2022-01-25 12:58:17

32

Views

Path-connectedness swapped definition

Published on 25 Jan 2022 - 12:58

score 44 · Answer 13 · 2022-01-25 16:53:05

$(X,\tau_X)$ is a path connected, then is there a continuous function from $(X,\tau_X)\rightarrow(\mathbb{R},\tau_E)$ with , $f(x)=0$ and $f(y)=1$

score 42 · Answer 14 · 2022-02-14 05:38:43

42

Views

Example for a set that is open connected but not path connected in an arbitrary topological space

Published on 14 Feb 2022 - 5:38

score 115 · Answer 15 · 2022-02-18 06:28:53

115

Views

If $X$ $\times$ $Y$ is path connected so is $X$ $\times$ $Y$ - $(x_0,y_0)$ for some $(x_0,y_0)$

Published on 18 Feb 2022 - 6:28

List Question

Is connected component of sublevel set of continuous function always path connected?

Path connected product topology implies every topology is path connected

How to show that this space is not path connected?

Locally connected for sub space topology of $\Bbb R^2$

Understanding the definition of path connected subspace

Is this graph connected or path-connected?

Is $\{ (x, y) \in \mathbb{C}^2 : x^2 + y^2 = 1\}$ connected in $\mathbb{C}^2$?

Trouble showing a union of sets is connected.

Connectedness of Hartogs' Triangle in $\mathbb C^2$

show that in $\mathbb{R}^2$ with the cofinite topology, every open set is both connected and path connected.

$C = (\{0\} \times [0,1]) \: \cup \: \{ (\frac{1}{n},y), n \in \mathbb{N}, y \in [0,1] \} \:\cup \: ([0,1] \times \{0\})$ is connected?

Path-connectedness swapped definition

$(X,\tau_X)$ is a path connected, then is there a continuous function from $(X,\tau_X)\rightarrow(\mathbb{R},\tau_E)$ with , $f(x)=0$ and $f(y)=1$

Example for a set that is open connected but not path connected in an arbitrary topological space

If $X$ $\times$ $Y$ is path connected so is $X$ $\times$ $Y$ - $(x_0,y_0)$ for some $(x_0,y_0)$

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