Question

Properties of covering spaces replacing base points by contractible subspaces

score 108 · Answer 1 · 2019-01-27 19:38:37

108

Views

Properties of covering spaces replacing base points by contractible subspaces

Published on 27 Jan 2019 - 19:38

score 160 · Answer 2 · 2019-06-11 20:56:12

160

Views

Homotopy Extension and Deformation Retracts

Published on 11 Jun 2019 - 20:56

score 748 · Answer 3 · 2019-08-10 16:47:36

748

Views

Question in Hatcher's Algebraic Topology Exercise 0.27

Published on 10 Aug 2019 - 16:47

score 75 · Answer 4 · 2019-08-30 14:18:45

75

Views

Proof that higher homotopy groups of kan complexes are abelian using Eckmann-Hilton

Published on 30 Aug 2019 - 14:18

score 819 · Answer 5 · 2019-11-28 17:24:04

819

Views

All finite path connected CW complexes are homotopy equivalent to a CW complex with only one 0-cell.

Published on 28 Nov 2019 - 17:24

score 409 · Answer 6 · 2020-01-09 17:54:23

409

Views

$(M_f, X \cup Y)$ has the homotopy extension property

Published on 09 Jan 2020 - 17:54

score 233 · Answer 7 · 2020-01-11 03:28:34

233

Views

Proving that two formulations of the Homotopy Extension Property via diagrams, are equivalent.

Published on 11 Jan 2020 - 3:28

score 171 · Answer 8 · 2020-03-06 15:50:48

171

Views

Show that either $X$ or $Z$ is homotopy equivalent to a point.

Published on 06 Mar 2020 - 15:50

score 609 · Answer 9 · 2020-05-15 16:44:31

609

Views

Hatcher Algebraic Topology 0.28

Published on 15 May 2020 - 16:44

score 33 · Answer 10 · 2020-05-17 13:53:17

33

Views

Prove that it is NOT $F_{0} \simeq_{S_{1} \cup 2 S_{1}} F_{1}$ for $F(x, t)= e^{2\pi t i (|x|-1)} x$

Published on 17 May 2020 - 13:53

score 374 · Answer 11 · 2020-05-18 14:35:30

374

Views

any cofibration $i:A \to B$ is a homeomorphism onto its image (question regarding the inverse map)

Published on 18 May 2020 - 14:35

score 70 · Answer 12 · 2020-05-19 00:00:19

70

Views

If a homotopy can be extended to a neighborhood of a closed subspace of a normal space $X$, then it can be extended to all of $X$.

Published on 19 May 2020 - 0:00

score 90 · Answer 13 · 2023-02-01 20:47:54

90

Views

Example where $(X,Y)$ and $(X,Z)$ have the homotopy extension property, but $(Y,Z)$ doesn't

Published on 01 Feb 2023 - 20:47

score 66 · Answer 14 · 2023-03-27 20:44:11

66

Views

Where can I get an alternative proof of this characterisation of weak equivalences?

Published on 27 Mar 2023 - 20:44

score 78 · Answer 15 · 2023-08-13 00:00:36

78

Views

When is a freely contractible space also based contractible?

Published on 13 Aug 2023 - 0:00

List Question

Properties of covering spaces replacing base points by contractible subspaces

Homotopy Extension and Deformation Retracts

Question in Hatcher's Algebraic Topology Exercise 0.27

Proof that higher homotopy groups of kan complexes are abelian using Eckmann-Hilton

All finite path connected CW complexes are homotopy equivalent to a CW complex with only one 0-cell.

$(M_f, X \cup Y)$ has the homotopy extension property

Proving that two formulations of the Homotopy Extension Property via diagrams, are equivalent.

Show that either $X$ or $Z$ is homotopy equivalent to a point.

Hatcher Algebraic Topology 0.28

Prove that it is NOT $F_{0} \simeq_{S_{1} \cup 2 S_{1}} F_{1}$ for $F(x, t)= e^{2\pi t i (|x|-1)} x$

any cofibration $i:A \to B$ is a homeomorphism onto its image (question regarding the inverse map)

If a homotopy can be extended to a neighborhood of a closed subspace of a normal space $X$, then it can be extended to all of $X$.

Example where $(X,Y)$ and $(X,Z)$ have the homotopy extension property, but $(Y,Z)$ doesn't

Where can I get an alternative proof of this characterisation of weak equivalences?

When is a freely contractible space also based contractible?

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