Question

The deleted comb space is connected and has two path components

score 134 · Answer 1 · 2020-10-06 02:06:37

134

Views

The deleted comb space is connected and has two path components

Published on 06 Oct 2020 - 2:06

score 81 · Answer 2 · 2020-10-06 22:03:42

81

Views

A function which is continuous on each path component is continuous

Published on 06 Oct 2020 - 22:03

score 529 · Answer 3 · 2020-10-10 20:54:37

529

Views

Show for any matrix $A$ with positive determinant, there is a continuous path in $GL_+(n,R)$ from $A$ to the identity.

Published on 10 Oct 2020 - 20:54

score 29 · Answer 4 · 2020-10-14 05:49:20

29

Views

For a connected two manifold and two points, there are at least two disjoint (except at endpoints) paths between the points?

Published on 14 Oct 2020 - 5:49

score 543 · Answer 5 · 2020-10-18 03:56:29

543

Views

Need the intersection of two path-connected subspaces be path-connected for their union to be path-connected?

Published on 18 Oct 2020 - 3:56

score 96 · Answer 6 · 2020-10-19 12:30:07

96

Views

Understanding topology and arc connectedness

Published on 19 Oct 2020 - 12:30

score 204 · Answer 7 · 2020-10-23 05:18:15

204

Views

Questions About Hawaiian Earring and Properties

Published on 23 Oct 2020 - 5:18

score 384 · Answer 8 · 2020-10-23 16:29:30

384

Views

Does every topological space have a fundamental group?

Published on 23 Oct 2020 - 16:29

score 201 · Answer 9 · 2020-10-24 16:12:47

201

Views

Show that a function $f : \mathbb R → \mathbb R$ is continuous if and only if its graph $[f]$ is path-connected

Published on 24 Oct 2020 - 16:12

score 283 · Answer 10 · 2020-10-25 05:38:25

283

Views

Prove that the set is path connected

Published on 25 Oct 2020 - 5:38

score 329 · Answer 11 · 2020-10-26 22:13:50

329

Views

Show that the plane with countably many points removed is path-connected under the Euclidean topology.

Published on 26 Oct 2020 - 22:13

score 132 · Answer 12 · 2020-10-29 01:47:29

132

Views

Prove fundamental group of R/~ is isomorphic to Z

Published on 29 Oct 2020 - 1:47

score 162 · Answer 13 · 2020-10-30 15:47:13

162

Views

connected but not path-connected sets

Published on 30 Oct 2020 - 15:47

score 284 · Answer 14 · 2020-11-02 19:46:01

284

Views

Computational example: Using the zeroth homology group to find the number of path components

Published on 02 Nov 2020 - 19:46

score 142 · Answer 15 · 2020-11-05 00:31:14

142

Views

Showing that the Sierpinski's Carpet is path-connected.

Published on 05 Nov 2020 - 0:31

List Question

The deleted comb space is connected and has two path components

A function which is continuous on each path component is continuous

Show for any matrix $A$ with positive determinant, there is a continuous path in $GL_+(n,R)$ from $A$ to the identity.

For a connected two manifold and two points, there are at least two disjoint (except at endpoints) paths between the points?

Need the intersection of two path-connected subspaces be path-connected for their union to be path-connected?

Understanding topology and arc connectedness

Questions About Hawaiian Earring and Properties

Does every topological space have a fundamental group?

Show that a function $f : \mathbb R → \mathbb R$ is continuous if and only if its graph $[f]$ is path-connected

Prove that the set is path connected

Show that the plane with countably many points removed is path-connected under the Euclidean topology.

Prove fundamental group of R/~ is isomorphic to Z

connected but not path-connected sets

Computational example: Using the zeroth homology group to find the number of path components

Showing that the Sierpinski's Carpet is path-connected.

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