Question

Dimension of domain is greater than/less than/equal to dimension of range for a smooth surjection/injection/submersion/immersion?

score 450 · Answer 1 · 2019-07-24 09:05:33

450

Views

Dimension of domain is greater than/less than/equal to dimension of range for a smooth surjection/injection/submersion/immersion?

Published on 24 Jul 2019 - 9:05

score 151 · Answer 2 · 2019-07-24 09:14:13

151

Views

Are open local embeddings equivalent to local diffeomorphisms? (Do not use immersions)

Published on 24 Jul 2019 - 9:14

score 953 · Answer 3 · 2019-08-27 22:14:24

953

Views

Deformation retraction arising from a mapping cylinder.

Published on 27 Aug 2019 - 22:14

score 37 · Answer 4 · 2019-08-27 23:39:35

37

Views

Changing the codomain in the definition of the retraction map.

Published on 27 Aug 2019 - 23:39

score 263 · Answer 5 · 2019-08-31 18:41:00

263

Views

A small discussion about Hatcher Q.1, chapter 0

Published on 31 Aug 2019 - 18:41

score 1.1k · Answer 6 · 2019-09-05 13:00:08

1.1k

Views

deformation retraction of the torus with 1 pt. deleted onto 2 circles intersecting at a pt. and that of $\mathbb R^n \setminus \{0\}$ onto $S^{n-1}$.

Published on 05 Sep 2019 - 13:00

score 40 · Answer 7 · 2019-09-21 13:27:23

40

Views

Does there exist two h-equal but not h-equivalent topological spaces?

Published on 21 Sep 2019 - 13:27

score 509 · Answer 8 · 2019-10-04 16:51:51

509

Views

There is no retraction map from unit disk to its boundary.(2)

Published on 04 Oct 2019 - 16:51

score 459 · Answer 9 · 2019-10-09 13:45:55

459

Views

Intuitively, why doesn't a ball retract to a sphere?

Published on 09 Oct 2019 - 13:45

score 75 · Answer 10 · 2019-10-28 00:08:44

75

Views

A compact Riemann surface with boundary strongly deformation retracting onto its boundary

Published on 28 Oct 2019 - 0:08

score 377 · Answer 11 · 2019-11-09 23:02:12

377

Views

A counter-example showing the inclusion $\{x_{0}\}\hookrightarrow X$ is a homotopy equivalence but $\{x_{0}\}$ is not a deformation retract of X

Published on 09 Nov 2019 - 23:02

score 69 · Answer 12 · 2019-12-03 22:44:58

69

Views

Are there any $\mathbf{Z}[x]$-algebra maps of the following form?

Published on 03 Dec 2019 - 22:44

score 328 · Answer 13 · 2020-01-03 21:04:15

328

Views

Subspace of $[0,1] \times [0,1]$ that deformation retracts to any point in $[0,1] \times \{0\}$, but not any other point.

Published on 03 Jan 2020 - 21:04

score 80 · Answer 14 · 2020-01-21 15:28:13

80

Views

Doubt in the proof of Lemma to prove No Retraction Theorem

Published on 21 Jan 2020 - 15:28

score 202 · Answer 15 · 2020-01-22 19:05:29

202

Views

Showing $S^1$ is not a retract of $\mathbb{D}^2$

Published on 22 Jan 2020 - 19:05

List Question

Dimension of domain is greater than/less than/equal to dimension of range for a smooth surjection/injection/submersion/immersion?

Are open local embeddings equivalent to local diffeomorphisms? (Do not use immersions)

Deformation retraction arising from a mapping cylinder.

Changing the codomain in the definition of the retraction map.

A small discussion about Hatcher Q.1, chapter 0

deformation retraction of the torus with 1 pt. deleted onto 2 circles intersecting at a pt. and that of $\mathbb R^n \setminus \{0\}$ onto $S^{n-1}$.

Does there exist two h-equal but not h-equivalent topological spaces?

There is no retraction map from unit disk to its boundary.(2)

Intuitively, why doesn't a ball retract to a sphere?

A compact Riemann surface with boundary strongly deformation retracting onto its boundary

A counter-example showing the inclusion $\{x_{0}\}\hookrightarrow X$ is a homotopy equivalence but $\{x_{0}\}$ is not a deformation retract of X

Are there any $\mathbf{Z}[x]$-algebra maps of the following form?

Subspace of $[0,1] \times [0,1]$ that deformation retracts to any point in $[0,1] \times \{0\}$, but not any other point.

Doubt in the proof of Lemma to prove No Retraction Theorem

Showing $S^1$ is not a retract of $\mathbb{D}^2$

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