Question

Queris related to "An arbitrary product $X=\prod_{\alpha \in J} X_\alpha$ is connected iff $X_{\alpha }$ is connected for each $\alpha\in J$."

score 109 · Answer 1 · 2026-03-25 22:05:24

109

Views

Queris related to "An arbitrary product $X=\prod_{\alpha \in J} X_\alpha$ is connected iff $X_{\alpha }$ is connected for each $\alpha\in J$."

Published on 25 Mar 2026 - 22:05

score 67 · Answer 2 · 2018-12-14 15:05:49

67

Views

Is the following exercise on connected subset wrong?

Published on 14 Dec 2018 - 15:05

score 70 · Answer 3 · 2026-03-25 12:50:08

70

Views

$|f(z)|=c\in\Bbb R\forall z\in\Omega$ for $\Omega\subset\Bbb C$ open and connected $\implies f$ is constant. Why must $\Omega$ be open, connected?

Published on 25 Mar 2026 - 12:50

score 568 · Answer 4 · 2018-12-22 03:13:23

568

Views

The interior of a disconnected set is disconnected?

Published on 22 Dec 2018 - 3:13

score 194 · Answer 5 · 2018-12-22 19:06:35

194

Views

If $f: M \to \mathbb{R}$ is a continuous function such that all values are irrationals, then $f$ is constant whenever $M$ is connected?

Published on 22 Dec 2018 - 19:06

score 77 · Answer 6 · 2018-12-23 23:11:44

77

Views

Show that if $f(-1)<0$ and $f(1)>0$, then there exist $-1<a<1$ such that $f(a)=0$

Published on 23 Dec 2018 - 23:11

score 283 · Answer 7 · 2018-12-24 00:46:59

283

Views

Is every nonopen connected subset of the circle path-connected?

Published on 24 Dec 2018 - 0:46

score 213 · Answer 8 · 2018-12-24 06:31:48

213

Views

A connected embedded submanifold, which is contained in an immersed submanifold, is connected in this submanifold?

Published on 24 Dec 2018 - 6:31

score 723 · Answer 9 · 2018-12-24 17:03:30

723

Views

How can I prove that $\mathbb Q \times \mathbb Q$ is connected?

Published on 24 Dec 2018 - 17:03

score 123 · Answer 10 · 2026-03-26 17:52:38

123

Views

When a subspace of a space is totally disconnected

Published on 26 Mar 2026 - 17:52

score 112 · Answer 11 · 2018-12-26 03:35:39

112

Views

Show that the closure of a connected set is connected.

Published on 26 Dec 2018 - 3:35

score 238 · Answer 12 · 2018-12-26 19:51:41

238

Views

The union of path-connected sets sharing a nonempty path-connected set $K$, is path-connected?

Published on 26 Dec 2018 - 19:51

score 28 · Answer 13 · 2018-12-26 20:14:19

28

Views

Connected space and his relathionship with his own subset

Published on 26 Dec 2018 - 20:14

score 76 · Answer 14 · 2026-03-27 20:12:00

76

Views

Exact differential forms defined in path connected sets

Published on 27 Mar 2026 - 20:12

score 796 · Answer 15 · 2018-12-30 07:03:00

796

Views

Assume $A \subset \mathbb{R}^n$ is connected such that $A^c$ is separated by $B,C$, then $A \cup B$ is connected.

Published on 30 Dec 2018 - 7:03

List Question

Queris related to "An arbitrary product $X=\prod_{\alpha \in J} X_\alpha$ is connected iff $X_{\alpha }$ is connected for each $\alpha\in J$."

Is the following exercise on connected subset wrong?

$|f(z)|=c\in\Bbb R\forall z\in\Omega$ for $\Omega\subset\Bbb C$ open and connected $\implies f$ is constant. Why must $\Omega$ be open, connected?

The interior of a disconnected set is disconnected?

If $f: M \to \mathbb{R}$ is a continuous function such that all values are irrationals, then $f$ is constant whenever $M$ is connected?

Show that if $f(-1)<0$ and $f(1)>0$, then there exist $-1<a<1$ such that $f(a)=0$

Is every nonopen connected subset of the circle path-connected?

A connected embedded submanifold, which is contained in an immersed submanifold, is connected in this submanifold?

How can I prove that $\mathbb Q \times \mathbb Q$ is connected?

When a subspace of a space is totally disconnected

Show that the closure of a connected set is connected.

The union of path-connected sets sharing a nonempty path-connected set $K$, is path-connected?

Connected space and his relathionship with his own subset

Exact differential forms defined in path connected sets

Assume $A \subset \mathbb{R}^n$ is connected such that $A^c$ is separated by $B,C$, then $A \cup B$ is connected.

Trending Questions

Popular # Hahtags

Popular Questions