Question

Degree of a circle map

score 314 · Answer 1 · 2026-04-12 04:18:45

314

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Degree of a circle map

Published on 12 Apr 2026 - 4:18

score 150 · Answer 2 · 2026-04-29 18:16:14

150

Views

When two objects are each other's retracts

Published on 29 Apr 2026 - 18:16

score 102 · Answer 3 · 2026-04-08 17:00:46

102

Views

An open in Banach space if connected if and only if is path-connected $C^{\infty}$

Published on 08 Apr 2026 - 17:00

score 69 · Answer 4 · 2026-04-26 18:49:54

69

Views

What are the consequences of alternative type-theoretic definition of homotopy equivalence?

Published on 26 Apr 2026 - 18:49

score 84 · Answer 5 · 2026-04-17 05:43:31

84

Views

Given a finite topological space $(\Omega, \tau)$ and $x \in \Omega$, show the smallest open set containing $x$ is homotopic to a point.

Published on 17 Apr 2026 - 5:43

score 214 · Answer 6 · 2026-04-11 10:53:20

214

Views

Show that loop in $S^1$ is not nullhomotopic

Published on 11 Apr 2026 - 10:53

score 115 · Answer 7 · 2026-04-13 06:44:03

115

Views

computing $\pi_1(\mathbb{R}P^2 \vee\mathbb{R}P^2)$ and $\pi_1(\mathbb{R}P^2 \times \mathbb{R}P^2)$

Published on 13 Apr 2026 - 6:44

score 585 · Answer 8 · 2026-04-16 09:30:51

585

Views

$X=S^2/{\sim}$ where any point on the equator is identified with its antipodal point. Compute $\pi_1(X)$ and $H_\ast(X)$

Published on 16 Apr 2026 - 9:30

score 613 · Answer 9 · 2026-04-15 18:11:04

613

Views

Compute $\pi_2(S^2 \vee S^2)$

Published on 15 Apr 2026 - 18:11

score 73 · Answer 10 · 2026-04-14 21:05:50

73

Views

Lifting problem of a functor along a Grothendieck fibrations in construction of homotopy colimits

Published on 14 Apr 2026 - 21:05

score 57 · Answer 11 · 2026-04-14 19:41:55

57

Views

Is $\{(x_1,x_2) \in \mathbb{R}^2 -\{(1,0)\} : x_1>-\frac{1}{2}\}$ homotopy equivalent to $\mathbb{R}^2-\{(0,0)\}$?

Published on 14 Apr 2026 - 19:41

score 194 · Answer 12 · 2026-04-11 14:07:38

194

Views

How can I prove that $[\sum X, Y] \cong [X, \Omega Y]$?

Published on 11 Apr 2026 - 14:07

score 134 · Answer 13 · 2026-04-26 12:53:16

134

Views

Is the nerve of a symmetric monoidal category a K-theory space?

Published on 26 Apr 2026 - 12:53

score 533 · Answer 14 · 2026-04-17 07:44:07

533

Views

Does the functor $\pi_n\colon \mathsf{Top}_* \to \mathsf{Grp}$ preserve products?

Published on 17 Apr 2026 - 7:44

score 486 · Answer 15 · 2026-04-15 23:20:45

486

Views

Surface of infinite genus deformation retracts onto a graph

Published on 15 Apr 2026 - 23:20

List Question

Degree of a circle map

When two objects are each other's retracts

An open in Banach space if connected if and only if is path-connected $C^{\infty}$

What are the consequences of alternative type-theoretic definition of homotopy equivalence?

Given a finite topological space $(\Omega, \tau)$ and $x \in \Omega$, show the smallest open set containing $x$ is homotopic to a point.

Show that loop in $S^1$ is not nullhomotopic

computing $\pi_1(\mathbb{R}P^2 \vee\mathbb{R}P^2)$ and $\pi_1(\mathbb{R}P^2 \times \mathbb{R}P^2)$

$X=S^2/{\sim}$ where any point on the equator is identified with its antipodal point. Compute $\pi_1(X)$ and $H_\ast(X)$

Compute $\pi_2(S^2 \vee S^2)$

Lifting problem of a functor along a Grothendieck fibrations in construction of homotopy colimits

Is $\{(x_1,x_2) \in \mathbb{R}^2 -\{(1,0)\} : x_1>-\frac{1}{2}\}$ homotopy equivalent to $\mathbb{R}^2-\{(0,0)\}$?

How can I prove that $[\sum X, Y] \cong [X, \Omega Y]$?

Is the nerve of a symmetric monoidal category a K-theory space?

Does the functor $\pi_n\colon \mathsf{Top}_* \to \mathsf{Grp}$ preserve products?

Surface of infinite genus deformation retracts onto a graph

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