List questions from homotopy-theory

Published on 10 Apr 2026 - 21:55

872

Views

Question about the definition of a fibration

Published on 11 Apr 2026 - 4:19

292

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One to one correspondence of $\langle X, Y\rangle $ and $\text{Hom}(\pi_n(X)),\pi_n(Y))$.

Published on 16 Apr 2026 - 15:44

320

Views

How to determine the homotopy class of a given path in $GL^+(n,\mathbb{R})$

Published on 12 Apr 2026 - 7:37

765

Views

Proving that the reduced mapping cylinder is deformation retract of space Y.

Published on 16 Apr 2026 - 2:55

61

Views

Sets homotopically equivalent

Published on 12 Apr 2026 - 20:28

154

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Show that there is a bijection between $[S^0,X]$ and $\pi_0(X)$ for a topological space X

Published on 15 Apr 2026 - 19:31

210

Views

Show that if $X$ is a pointed retract of $Y$, and $Y$ is a $H$-space, then $X$ is a $H$-space too.

Published on 13 Apr 2026 - 20:34

344

Views

Covering map, right cosets and sheets.

Published on 15 Apr 2026 - 2:45

167

Views

Question on Fibration

Published on 30 Apr 2026 - 6:20

1k

Views

Composition and Product of fibrations

Published on 12 Apr 2026 - 11:12

115

Views

Question on Homotopy

Published on 12 Apr 2026 - 9:06

87

Views

May's Alge' Top', Dependence on base point explanation

Published on 14 Apr 2026 - 13:07

197

Views

path connectedness of a preimage

Published on 11 Apr 2026 - 10:01

218

Views

If $f:\mathbb R \to \mathbb R^n$ is injective, is $f(\mathbb R)$ contractible?

Published on 16 Apr 2026 - 2:28

List Question

Linking numbers.

Question about the definition of a fibration

One to one correspondence of $\langle X, Y\rangle $ and $\text{Hom}(\pi_n(X)),\pi_n(Y))$.

How to determine the homotopy class of a given path in $GL^+(n,\mathbb{R})$

Proving that the reduced mapping cylinder is deformation retract of space Y.

Sets homotopically equivalent

Show that there is a bijection between $[S^0,X]$ and $\pi_0(X)$ for a topological space X

Show that if $X$ is a pointed retract of $Y$, and $Y$ is a $H$-space, then $X$ is a $H$-space too.

Covering map, right cosets and sheets.

Question on Fibration

Composition and Product of fibrations

Question on Homotopy

May's Alge' Top', Dependence on base point explanation

path connectedness of a preimage

If $f:\mathbb R \to \mathbb R^n$ is injective, is $f(\mathbb R)$ contractible?

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