Question

Which of the given subsets of the vector space $\mathbb R^3$ are connected.

score 97 · Answer 1 · 2016-11-30 06:46:26

97

Views

Which of the given subsets of the vector space $\mathbb R^3$ are connected.

Published on 30 Nov 2016 - 6:46

score 626 · Answer 2 · 2026-03-23 13:22:34

626

Views

Simple connectedness of basin of attraction

Published on 23 Mar 2026 - 13:22

score 107 · Answer 3 · 2016-12-04 18:06:02

107

Views

$X$ topological space and $S\subseteq X$ and $\overline{S}=X$. Show that if $S$ is connected, then $X$ is also

Published on 04 Dec 2016 - 18:06

score 177 · Answer 4 · 2016-12-05 06:28:34

177

Views

If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $

Published on 05 Dec 2016 - 6:28

score 1.7k · Answer 5 · 2016-12-06 00:06:41

1.7k

Views

$\nabla U=0 \implies U=\mathrm{constant}$ only if $U$ is defined on a connected set?

Published on 06 Dec 2016 - 0:06

score 57 · Answer 6 · 2026-03-28 10:28:06

57

Views

quotient space of $\Bbb S^3$

Published on 28 Mar 2026 - 10:28

score 327 · Answer 7 · 2016-12-09 15:36:07

327

Views

Prove that $D$ is connected if the set $\{(x,f(x)):x\in D\}$,the graph of $f$ is a connected subset of $\Bbb R^2$

Published on 09 Dec 2016 - 15:36

score 187 · Answer 8 · 2026-03-27 10:33:03

187

Views

Connected but not path connected

Published on 27 Mar 2026 - 10:33

score 634 · Answer 9 · 2016-12-12 02:23:27

634

Views

Topology question. Which of the following subsets are open? closed? connected? Compact?

Published on 12 Dec 2016 - 2:23

score 838 · Answer 10 · 2016-12-19 18:42:00

838

Views

Path connectedness of the set $\{(x,y):(x+1)^{2}+y^{2}\leq 1\}\cup\{(x,y):y=x\sin(\frac{1}{x}),x>0\}$

Published on 19 Dec 2016 - 18:42

score 37 · Answer 11 · 2016-12-20 04:50:07

37

Views

If $p_0 \in X$, $\{d(p_0, q): q \in X\}$ is either equal to $\{0\}$ or is an interval containing $0$

Published on 20 Dec 2016 - 4:50

score 946 · Answer 12 · 2016-12-21 21:14:41

946

Views

Connected topological space such that the removal of any of its points disconnects it into exactly $3$ connected components?

Published on 21 Dec 2016 - 21:14

score 1.1k · Answer 13 · 2016-12-25 20:27:30

1.1k

Views

Show that Brooks' theorem is equivalent to the following:

Published on 25 Dec 2016 - 20:27

score 144 · Answer 14 · 2016-12-28 19:21:10

144

Views

Connected set exercise/proof

Published on 28 Dec 2016 - 19:21

score 459 · Answer 15 · 2016-12-29 03:49:13

459

Views

Basis that generates a topology for a connected topological space

Published on 29 Dec 2016 - 3:49

List Question

Which of the given subsets of the vector space $\mathbb R^3$ are connected.

Simple connectedness of basin of attraction

$X$ topological space and $S\subseteq X$ and $\overline{S}=X$. Show that if $S$ is connected, then $X$ is also

If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $

$\nabla U=0 \implies U=\mathrm{constant}$ only if $U$ is defined on a connected set?

quotient space of $\Bbb S^3$

Prove that $D$ is connected if the set $\{(x,f(x)):x\in D\}$,the graph of $f$ is a connected subset of $\Bbb R^2$

Connected but not path connected

Topology question. Which of the following subsets are open? closed? connected? Compact?

Path connectedness of the set $\{(x,y):(x+1)^{2}+y^{2}\leq 1\}\cup\{(x,y):y=x\sin(\frac{1}{x}),x>0\}$

If $p_0 \in X$, $\{d(p_0, q): q \in X\}$ is either equal to $\{0\}$ or is an interval containing $0$

Connected topological space such that the removal of any of its points disconnects it into exactly $3$ connected components?

Show that Brooks' theorem is equivalent to the following:

Connected set exercise/proof

Basis that generates a topology for a connected topological space

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