Question

The union of two disjoint non-empty open sets is not path-connected?

score 1k · Answer 1 · 2017-11-11 17:09:07

1k

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The union of two disjoint non-empty open sets is not path-connected?

Published on 11 Nov 2017 - 17:09

score 211 · Answer 2 · 2026-03-26 16:56:39

211

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Show that a graph can be separated in k disjoint trails but with at most one trail of length odd.

Published on 26 Mar 2026 - 16:56

score 146 · Answer 3 · 2017-11-14 23:35:25

146

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When does path connectedness imply local path connectedness?

Published on 14 Nov 2017 - 23:35

score 131 · Answer 4 · 2017-11-28 17:49:32

131

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Proof: A open connected subspace of $\mathbb{R}^2$ is path Connected.

Published on 28 Nov 2017 - 17:49

score 690 · Answer 5 · 2017-11-29 23:43:50

690

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Number of Paths from A to B

Published on 29 Nov 2017 - 23:43

score 976 · Answer 6 · 2017-12-05 16:54:38

976

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Show that $\mathbb{R}^{n}$ ($n>2$) minus a countable number of lines is still path-connected

Published on 05 Dec 2017 - 16:54

score 3.5k · Answer 7 · 2017-12-09 06:28:09

3.5k

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If $A$ countable then $\Bbb{R}^2\setminus A$ is path connected

Published on 09 Dec 2017 - 6:28

score 195 · Answer 8 · 2017-12-13 14:15:39

195

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$X \setminus point$ not path-connected implies $X$ simply connected

Published on 13 Dec 2017 - 14:15

score 350 · Answer 9 · 2017-12-13 22:46:37

350

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How to use a continuous function on $[0,1]$ to prove another set is connected?

Published on 13 Dec 2017 - 22:46

score 125 · Answer 10 · 2017-12-19 16:24:21

125

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Estimating distance to travel to each household in a county

Published on 19 Dec 2017 - 16:24

score 950 · Answer 11 · 2017-12-22 20:06:17

950

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function with path connected graph

Published on 22 Dec 2017 - 20:06

score 1.6k · Answer 12 · 2017-12-23 09:05:15

1.6k

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Show that the special orthogonal group $SO_n(\mathbb{R})$ is arcwise connected and compact

Published on 23 Dec 2017 - 9:05

score 141 · Answer 13 · 2017-12-27 11:04:26

141

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$A,B$ subsets of euclidean space, $A$ convex, $B$ path connected and closure of $A$ has a point in common with $B$

Published on 27 Dec 2017 - 11:04

score 1.4k · Answer 14 · 2017-12-31 00:49:13

1.4k

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Path-connected does not imply convex

Published on 31 Dec 2017 - 0:49

score 433 · Answer 15 · 2018-01-03 08:55:43

433

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Example 2, Sec. 25, in Munkres' TOPOLOGY, 2nd ed: The Topologist's Sine Curve

Published on 03 Jan 2018 - 8:55

List Question

The union of two disjoint non-empty open sets is not path-connected?

Show that a graph can be separated in k disjoint trails but with at most one trail of length odd.

When does path connectedness imply local path connectedness?

Proof: A open connected subspace of $\mathbb{R}^2$ is path Connected.

Number of Paths from A to B

Show that $\mathbb{R}^{n}$ ($n>2$) minus a countable number of lines is still path-connected

If $A$ countable then $\Bbb{R}^2\setminus A$ is path connected

$X \setminus point$ not path-connected implies $X$ simply connected

How to use a continuous function on $[0,1]$ to prove another set is connected?

Estimating distance to travel to each household in a county

function with path connected graph

Show that the special orthogonal group $SO_n(\mathbb{R})$ is arcwise connected and compact

$A,B$ subsets of euclidean space, $A$ convex, $B$ path connected and closure of $A$ has a point in common with $B$

Path-connected does not imply convex

Example 2, Sec. 25, in Munkres' TOPOLOGY, 2nd ed: The Topologist's Sine Curve

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