Question

Connected and locally path connected

score 10.3k · Answer 1 · 2016-08-01 23:38:33

10.3k

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Connected and locally path connected

Published on 01 Aug 2016 - 23:38

score 1.7k · Answer 2 · 2016-08-02 22:02:28

1.7k

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When is a disconnected subset of a topological space 'disconnected in the total space'?

Published on 02 Aug 2016 - 22:02

score 66 · Answer 3 · 2026-03-31 14:12:58

66

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Why paths are defined on connected subsets of $\mathbb{R}$?

Published on 31 Mar 2026 - 14:12

score 187 · Answer 4 · 2026-03-27 07:17:16

187

Views

$X$ be a topological space , then is it true that every connected component of $X$ is a union of path-connected components?

Published on 27 Mar 2026 - 7:17

score 429 · Answer 5 · 2016-08-06 19:34:49

429

Views

Show that if $X$ is disconnected (with $\overline A \cap B = A \cap \overline B = \varnothing$), then there exists disjoint open sets

Published on 06 Aug 2016 - 19:34

score 1.3k · Answer 6 · 2016-08-06 20:18:47

1.3k

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Components vs Quasicomponents

Published on 06 Aug 2016 - 20:18

score 751 · Answer 7 · 2016-08-07 00:41:19

751

Views

Given $X$ compact and Hausdorff, $C$ a component of $X$, and $U$ open set containing $C$, show that $\exists V$ clopen such that $C\subset V\subset U$

Published on 07 Aug 2016 - 0:41

score 273 · Answer 8 · 2016-08-08 16:00:27

273

Views

Characterization of connectedness for subspaces

Published on 08 Aug 2016 - 16:00

score 1.7k · Answer 9 · 2026-03-27 08:38:40

1.7k

Views

Is $\mathbb R$ endowed with countable complement topology path connected ?

Published on 27 Mar 2026 - 8:38

score 466 · Answer 10 · 2016-08-10 09:51:37

466

Views

About the topology of the Heisenberg group

Published on 10 Aug 2016 - 9:51

score 50 · Answer 11 · 2026-03-26 06:07:58

50

Views

$X$ non-degenerate Hausdorff space , $f:[0,1] \to X$ is surjective continuous , $a:=\inf \{y\in (0,1]: f([0,y])=X\}$ , then is $a>0$ and $f([0,a])=X$?

Published on 26 Mar 2026 - 6:07

score 597 · Answer 12 · 2016-08-10 19:06:43

597

Views

Square as union of two disjoint connected sets containing opposite corners

Published on 10 Aug 2016 - 19:06

score 549 · Answer 13 · 2016-08-11 05:51:11

549

Views

If a space is connected in a topology, given a coarser topology, is it connected?

Published on 11 Aug 2016 - 5:51

score 63 · Answer 14 · 2026-03-26 12:37:50

63

Views

Which members of a particular family of graphs are either connected or planar?

Published on 26 Mar 2026 - 12:37

score 617 · Answer 15 · 2016-08-12 17:08:59

617

Views

A topological space such that every subspace from it is connected.

Published on 12 Aug 2016 - 17:08

List Question

Connected and locally path connected

When is a disconnected subset of a topological space 'disconnected in the total space'?

Why paths are defined on connected subsets of $\mathbb{R}$?

$X$ be a topological space , then is it true that every connected component of $X$ is a union of path-connected components?

Show that if $X$ is disconnected (with $\overline A \cap B = A \cap \overline B = \varnothing$), then there exists disjoint open sets

Components vs Quasicomponents

Given $X$ compact and Hausdorff, $C$ a component of $X$, and $U$ open set containing $C$, show that $\exists V$ clopen such that $C\subset V\subset U$

Characterization of connectedness for subspaces

Is $\mathbb R$ endowed with countable complement topology path connected ?

About the topology of the Heisenberg group

$X$ non-degenerate Hausdorff space , $f:[0,1] \to X$ is surjective continuous , $a:=\inf \{y\in (0,1]: f([0,y])=X\}$ , then is $a>0$ and $f([0,a])=X$?

Square as union of two disjoint connected sets containing opposite corners

If a space is connected in a topology, given a coarser topology, is it connected?

Which members of a particular family of graphs are either connected or planar?

A topological space such that every subspace from it is connected.

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