Question

Let $f : B^2 \rightarrow \mathbb{R}^2$ a continuous map, is $B^2 \subset \operatorname{im}(f)$?

score 107 · Answer 1 · 2026-03-26 11:05:08

107

Views

Let $f : B^2 \rightarrow \mathbb{R}^2$ a continuous map, is $B^2 \subset \operatorname{im}(f)$?

Published on 26 Mar 2026 - 11:05

score 944 · Answer 2 · 2026-04-13 04:18:39

944

Views

Center of fundamental group

Published on 13 Apr 2026 - 4:18

score 947 · Answer 3 · 2019-04-29 00:44:33

947

Views

Prove that if $f$ is not surjective, then $f$ is homotopic to a constant via a homotopy that fixes a point

Published on 29 Apr 2019 - 0:44

score 885 · Answer 4 · 2026-04-12 18:14:28

885

Views

Why does the Betti number give the measure of k-dimensional holes?

Published on 12 Apr 2026 - 18:14

score 245 · Answer 5 · 2026-04-12 20:36:29

245

Views

How is the generator of the first homology of the torus non-trivial?

Published on 12 Apr 2026 - 20:36

score 142 · Answer 6 · 2026-04-13 02:05:26

142

Views

A reference for an explicit statement of the Galois correspondence in a Galois category

Published on 13 Apr 2026 - 2:05

score 1.7k · Answer 7 · 2026-04-11 22:36:48

1.7k

Views

Relationship between Betti number and Genus

Published on 11 Apr 2026 - 22:36

score 316 · Answer 8 · 2019-04-30 03:53:03

Let $f: \Bbb S^2 \rightarrow \Bbb RP^2$ and $g: \Bbb RP^2 \rightarrow \Bbb S^2$ be continuous maps between sphere and projective plane.

score 251 · Answer 9 · 2019-04-30 05:46:06

251

Views

The solid torus $X$ is the solid of revolution in $\mathbb R^3$ gotten by revolving the circle around the z axis

Published on 30 Apr 2019 - 5:46

score 304 · Answer 10 · 2026-04-11 12:22:04

304

Views

Using universal coverings to calculate fundamental group

Published on 11 Apr 2026 - 12:22

score 806 · Answer 11 · 2026-04-11 18:13:50

806

Views

Can we divide $\mathbb{R}^2$ into two path connected parts such that each part is not simply-connected?

Published on 11 Apr 2026 - 18:13

score 80 · Answer 12 · 2026-03-25 07:47:57

80

Views

Factorization of the orientation map $MU\to H\mathbb{Z}$ through $ku$?

Published on 25 Mar 2026 - 7:47

score 253 · Answer 13 · 2026-03-25 17:24:51

253

Views

How is the Tonnetz grid isomorphic to a torus?

Published on 25 Mar 2026 - 17:24

score 172 · Answer 14 · 2026-04-11 21:08:35

172

Views

The cohomology ring of two tori glued along the first circle

Published on 11 Apr 2026 - 21:08

score 67 · Answer 15 · 2026-03-25 12:52:06

67

Views

Is it true that $\pi_1(M)=\langle a\mid aaa,aa^{-1} \rangle \cong \Bbb Z_3$?

Published on 25 Mar 2026 - 12:52

List Question

Let $f : B^2 \rightarrow \mathbb{R}^2$ a continuous map, is $B^2 \subset \operatorname{im}(f)$?

Center of fundamental group

Prove that if $f$ is not surjective, then $f$ is homotopic to a constant via a homotopy that fixes a point

Why does the Betti number give the measure of k-dimensional holes?

How is the generator of the first homology of the torus non-trivial?

A reference for an explicit statement of the Galois correspondence in a Galois category

Relationship between Betti number and Genus

Let $f: \Bbb S^2 \rightarrow \Bbb RP^2$ and $g: \Bbb RP^2 \rightarrow \Bbb S^2$ be continuous maps between sphere and projective plane.

The solid torus $X$ is the solid of revolution in $\mathbb R^3$ gotten by revolving the circle around the z axis

Using universal coverings to calculate fundamental group

Can we divide $\mathbb{R}^2$ into two path connected parts such that each part is not simply-connected?

Factorization of the orientation map $MU\to H\mathbb{Z}$ through $ku$?

How is the Tonnetz grid isomorphic to a torus?

The cohomology ring of two tori glued along the first circle

Is it true that $\pi_1(M)=\langle a\mid aaa,aa^{-1} \rangle \cong \Bbb Z_3$?

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