Question

Prove that there is a plane in $\mathbb{R}^n$ with the following property

score 407 · Answer 1 · 2017-02-23 19:25:17

407

Views

Prove that there is a plane in $\mathbb{R}^n$ with the following property

Published on 23 Feb 2017 - 19:25

score 330 · Answer 2 · 2017-02-24 00:11:55

330

Views

Must the complement of countably many disjoint arcs be connected?

Published on 24 Feb 2017 - 0:11

score 316 · Answer 3 · 2026-03-26 12:34:41

316

Views

How do the subgroups of $(\mathbb C,+)$ which are connected (path connected) in $\mathbb C$ look like?

Published on 26 Mar 2026 - 12:34

score 66 · Answer 4 · 2017-03-01 16:06:46

66

Views

The only proper subfield of $\mathbb C$ , which is path connected as a subset of $\mathbb C$ , must be $\mathbb R$?

Published on 01 Mar 2017 - 16:06

score 66 · Answer 5 · 2017-03-03 13:46:45

66

Views

Can every path connected $1$-surface in $\mathbb R^{n+1}$ be globally parametrized?

Published on 03 Mar 2017 - 13:46

score 191 · Answer 6 · 2017-03-10 14:05:32

191

Views

Is any path connected component of an $n$-surface in $\mathbb R^{n+k}$ again an $n$ -surface?

Published on 10 Mar 2017 - 14:05

score 904 · Answer 7 · 2026-03-25 16:01:48

904

Views

I know every path is a walk. But how do I prove the following question?

Published on 25 Mar 2026 - 16:01

score 329 · Answer 8 · 2017-03-12 13:43:12

329

Views

$W$ be an $m$-dimensional linear subspace of $\mathbb R^n$ such that $m\le n-2$ , then is it true that $\mathbb R^n \setminus W$ is connected?

Published on 12 Mar 2017 - 13:43

score 1k · Answer 9 · 2017-03-14 13:35:51

1k

Views

Path connectedness as an equivalence relation

Published on 14 Mar 2017 - 13:35

score 1.2k · Answer 10 · 2017-03-16 10:07:35

1.2k

Views

Topological group needs to be path connected

Published on 16 Mar 2017 - 10:07

score 329 · Answer 11 · 2017-03-16 17:10:03

329

Views

Shortest path by colored flips

Published on 16 Mar 2017 - 17:10

score 195 · Answer 12 · 2026-03-25 23:16:14

195

Views

path connectedness of a preimage

Published on 25 Mar 2026 - 23:16

score 516 · Answer 13 · 2026-02-23 01:08:27

516

Views

Is the property of local connectedness or local path-connectedness invariant under homotopy equivalence?

Published on 23 Feb 2026 - 1:08

score 43 · Answer 14 · 2017-03-20 12:57:16

43

Views

If $W$ is path connected and $W \subseteq U$ with $U$ open, then there exists $V$ open and connected such that $W \subseteq V \subseteq U$?

Published on 20 Mar 2017 - 12:57

score 68 · Answer 15 · 2017-03-21 17:55:19

68

Views

Erdos Number Technicalities

Published on 21 Mar 2017 - 17:55

List Question

Prove that there is a plane in $\mathbb{R}^n$ with the following property

Must the complement of countably many disjoint arcs be connected?

How do the subgroups of $(\mathbb C,+)$ which are connected (path connected) in $\mathbb C$ look like?

The only proper subfield of $\mathbb C$ , which is path connected as a subset of $\mathbb C$ , must be $\mathbb R$?

Can every path connected $1$-surface in $\mathbb R^{n+1}$ be globally parametrized?

Is any path connected component of an $n$-surface in $\mathbb R^{n+k}$ again an $n$ -surface?

I know every path is a walk. But how do I prove the following question?

$W$ be an $m$-dimensional linear subspace of $\mathbb R^n$ such that $m\le n-2$ , then is it true that $\mathbb R^n \setminus W$ is connected?

Path connectedness as an equivalence relation

Topological group needs to be path connected

Shortest path by colored flips

path connectedness of a preimage

Is the property of local connectedness or local path-connectedness invariant under homotopy equivalence?

If $W$ is path connected and $W \subseteq U$ with $U$ open, then there exists $V$ open and connected such that $W \subseteq V \subseteq U$?

Erdos Number Technicalities

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