Question

simply connected subset of $\mathbb R^2$ contractible?

score 430 · Answer 1 · 2017-10-05 18:51:45

430

Views

simply connected subset of $\mathbb R^2$ contractible?

Published on 05 Oct 2017 - 18:51

score 871 · Answer 2 · 2017-10-10 06:00:14

871

Views

Find a topological space $X$ which is connected but has three path components.

Published on 10 Oct 2017 - 6:00

score 323 · Answer 3 · 2017-10-10 06:25:40

323

Views

Let $X$ be obtained by removing finitely many lines from $\mathbb{R}^3$. How do I prove $X$ is connected?

Published on 10 Oct 2017 - 6:25

score 29 · Answer 4 · 2017-10-11 22:42:18

29

Views

For all norms on $\mathbb{R}^n$, for all $x\in\mathbb{R}^n$, for all $r > 0$, for all $y, z \in B(x,r)$, the line segment $[y, z) \subseteq B(x,r)$.

Published on 11 Oct 2017 - 22:42

score 462 · Answer 5 · 2017-10-14 22:46:34

462

Views

Proving that the set of all invertible diagonal matrices over $\mathbb{C}$ is a path connected subset of $\mathbb{C}^{n^2}$

Published on 14 Oct 2017 - 22:46

score 58 · Answer 6 · 2017-10-22 00:29:26

58

Views

For $r$ obeying $r>0$ and $r\neq 1$, set $I(r)=\int_{|z|=r}(z^2+1)^{-1}\operatorname{Log}z \, dz$.

Published on 22 Oct 2017 - 0:29

score 649 · Answer 7 · 2026-03-27 08:55:59

649

Views

Show that $X=\prod X_\alpha$ is path connected if and only if each $X_\alpha$ is path connected

Published on 27 Mar 2026 - 8:55

score 234 · Answer 8 · 2017-10-24 14:17:23

234

Views

Strengthening of the Jordan curve theorem

Published on 24 Oct 2017 - 14:17

score 522 · Answer 9 · 2017-10-26 10:19:53

522

Views

Number of components in a covering space is less than or equal to number of sheets?

Published on 26 Oct 2017 - 10:19

score 668 · Answer 10 · 2017-10-26 21:43:50

668

Views

Connected component of identity and normal subgroups

Published on 26 Oct 2017 - 21:43

score 107 · Answer 11 · 2017-10-27 06:25:06

107

Views

Connectivity of the space of simple $n$-polylines in the plane

Published on 27 Oct 2017 - 6:25

score 1.3k · Answer 12 · 2017-10-31 04:28:07

1.3k

Views

Show a certain finite topological space is path connected

Published on 31 Oct 2017 - 4:28

score 175 · Answer 13 · 2017-10-31 10:07:16

175

Views

connected path manifold is connected

Published on 31 Oct 2017 - 10:07

score 109 · Answer 14 · 2026-02-23 02:47:18

109

Views

Path-connected components of the configuration space $F_n(R^d)$

Published on 23 Feb 2026 - 2:47

score 680 · Answer 15 · 2026-03-27 08:58:56

680

Views

Is $\Bbb{R}^\omega$ (with uniform topology) locally path connected?

Published on 27 Mar 2026 - 8:58

List Question

simply connected subset of $\mathbb R^2$ contractible?

Find a topological space $X$ which is connected but has three path components.

Let $X$ be obtained by removing finitely many lines from $\mathbb{R}^3$. How do I prove $X$ is connected?

For all norms on $\mathbb{R}^n$, for all $x\in\mathbb{R}^n$, for all $r > 0$, for all $y, z \in B(x,r)$, the line segment $[y, z) \subseteq B(x,r)$.

Proving that the set of all invertible diagonal matrices over $\mathbb{C}$ is a path connected subset of $\mathbb{C}^{n^2}$

For $r$ obeying $r>0$ and $r\neq 1$, set $I(r)=\int_{|z|=r}(z^2+1)^{-1}\operatorname{Log}z \, dz$.

Show that $X=\prod X_\alpha$ is path connected if and only if each $X_\alpha$ is path connected

Strengthening of the Jordan curve theorem

Number of components in a covering space is less than or equal to number of sheets?

Connected component of identity and normal subgroups

Connectivity of the space of simple $n$-polylines in the plane

Show a certain finite topological space is path connected

connected path manifold is connected

Path-connected components of the configuration space $F_n(R^d)$

Is $\Bbb{R}^\omega$ (with uniform topology) locally path connected?

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