Question

$C(X) := X \times [0,1]/ \sim $, when $(x_1,0) \sim (x_2,0)$ is connected.

score 118 · Answer 1 · 2026-03-28 14:07:38

118

Views

$C(X) := X \times [0,1]/ \sim $, when $(x_1,0) \sim (x_2,0)$ is connected.

Published on 28 Mar 2026 - 14:07

score 519 · Answer 2 · 2017-01-21 19:11:01

519

Views

A topological space is path connected if and only if the associated graph is connected

Published on 21 Jan 2017 - 19:11

score 232 · Answer 3 · 2026-03-27 10:34:24

232

Views

Are there generalizations of "connectedness $\implies$ path-connectedness" in $\mathbb{R}^n$?

Published on 27 Mar 2026 - 10:34

score 210 · Answer 4 · 2026-04-01 05:04:00

210

Views

Check whether domain and range of non constant function $f$ from connected space $X$ to $\Bbb{R}$ is countable or uncountable. ( GATE 2015)

Published on 01 Apr 2026 - 5:04

score 65 · Answer 5 · 2017-01-25 03:33:29

65

Views

Does the number $\sup\{t\in [0,1]:[0,t]\subseteq U\}$ even exist?

Published on 25 Jan 2017 - 3:33

score 112 · Answer 6 · 2017-01-25 13:21:08

112

Views

Open connected components

Published on 25 Jan 2017 - 13:21

score 260 · Answer 7 · 2017-01-25 19:41:29

260

Views

Showing a Subset of $\mathbb{R}^2$ is not Connected

Published on 25 Jan 2017 - 19:41

score 761 · Answer 8 · 2017-01-26 01:56:25

761

Views

Proving that if $E\subseteq \mathbb{R}^n$ is open and connected then it is path-connected

Published on 26 Jan 2017 - 1:56

score 2.5k · Answer 9 · 2017-01-26 05:08:09

2.5k

Views

Prove that the intersection of a nested sequence of connected, compact subsets of the plane is connected

Published on 26 Jan 2017 - 5:08

score 57 · Answer 10 · 2017-01-26 16:53:12

57

Views

For every separation $X= A \cup B$, $x_1, x_2$ are both in $A$ or $B$. Ex.: $x_1$ and $x_2$ not in same component.

Published on 26 Jan 2017 - 16:53

score 777 · Answer 11 · 2017-01-26 20:46:52

777

Views

Mathematical meaning of shrinking a loop to a point

Published on 26 Jan 2017 - 20:46

score 55 · Answer 12 · 2017-01-28 10:10:47

55

Views

Continuity on a Domain and Local Connectedness

Published on 28 Jan 2017 - 10:10

score 1.2k · Answer 13 · 2017-01-29 14:20:11

1.2k

Views

countable intersection of connected sets

Published on 29 Jan 2017 - 14:20

score 35 · Answer 14 · 2017-01-31 12:58:12

35

Views

In a Banach space, for each point the collection of all scalar multipliers of this point is connected, how to prove?

Published on 31 Jan 2017 - 12:58

score 38 · Answer 15 · 2017-02-01 20:44:41

38

Views

Is this space connected, locally connected?

Published on 01 Feb 2017 - 20:44

List Question

$C(X) := X \times [0,1]/ \sim $, when $(x_1,0) \sim (x_2,0)$ is connected.

A topological space is path connected if and only if the associated graph is connected

Are there generalizations of "connectedness $\implies$ path-connectedness" in $\mathbb{R}^n$?

Check whether domain and range of non constant function $f$ from connected space $X$ to $\Bbb{R}$ is countable or uncountable. ( GATE 2015)

Does the number $\sup\{t\in [0,1]:[0,t]\subseteq U\}$ even exist?

Open connected components

Showing a Subset of $\mathbb{R}^2$ is not Connected

Proving that if $E\subseteq \mathbb{R}^n$ is open and connected then it is path-connected

Prove that the intersection of a nested sequence of connected, compact subsets of the plane is connected

For every separation $X= A \cup B$, $x_1, x_2$ are both in $A$ or $B$. Ex.: $x_1$ and $x_2$ not in same component.

Mathematical meaning of shrinking a loop to a point

Continuity on a Domain and Local Connectedness

countable intersection of connected sets

In a Banach space, for each point the collection of all scalar multipliers of this point is connected, how to prove?

Is this space connected, locally connected?

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