Question

In general, how do you prove that a topological space isn’t a retraction of another?

score 96 · Answer 1 · 2022-02-27 12:50:45

96

Views

In general, how do you prove that a topological space isn’t a retraction of another?

Published on 27 Feb 2022 - 12:50

score 196 · Answer 2 · 2022-03-18 12:20:59

196

Views

Almost retracting a ball to its boundary

Published on 18 Mar 2022 - 12:20

score 146 · Answer 3 · 2022-05-03 16:35:55

146

Views

Showing there is a retraction from $\Bbb R^2$ to the closed disk $D$

Published on 03 May 2022 - 16:35

score 36 · Answer 4 · 2022-06-04 22:24:04

36

Views

Question about homotopy equivalence (Hatcher $0.4$)

Published on 04 Jun 2022 - 22:24

score 86 · Answer 5 · 2022-06-11 20:09:45

86

Views

Show that retraction is coequalizer.

Published on 11 Jun 2022 - 20:09

score 225 · Answer 6 · 2022-06-19 09:36:11

225

Views

Explicit retraction of $\mathbb{R}^n$ minus $k$ points to wedge sum of $k$ copies of $S^{(n-1)}$

Published on 19 Jun 2022 - 9:36

score 170 · Answer 7 · 2022-07-04 13:48:31

170

Views

Does finitely generated groups have finitely many finite retracts?

Published on 04 Jul 2022 - 13:48

score 72 · Answer 8 · 2022-07-12 08:20:15

72

Views

If $Y \subseteq Q$ is a retract of the Hilbert cube $Q$ and $Z \subseteq Q$ is homeomorphic to $Y$, is $Z$ a retract of $Q$?

Published on 12 Jul 2022 - 8:20

score 389 · Answer 9 · 2022-07-15 18:02:12

389

Views

$\Bbb{R}^3 - S^1$ deformation retracts to $S^2 \vee S^1$?

Published on 15 Jul 2022 - 18:02

score 226 · Answer 10 · 2022-07-29 23:09:32

226

Views

Fundamental group of the boundary of a torus with a point removed

Published on 29 Jul 2022 - 23:09

score 92 · Answer 11 · 2022-08-03 02:12:26

92

Views

Are there any topological spaces containing no proper retracts? i.e. $A\subset X$ s.t. $\exists r:X\to A$ continuous w/ $r(a)=a,\forall a\in A$

Published on 03 Aug 2022 - 2:12

score 109 · Answer 12 · 2022-08-11 15:05:19

109

Views

Does a free group $F$ of finite rank $n$ have finitely many retracts (as a subgroup)?

Published on 11 Aug 2022 - 15:05

score 94 · Answer 13 · 2022-08-20 11:50:24

94

Views

The number of retracts of $G\ltimes \mathbb{Z}$

Published on 20 Aug 2022 - 11:50

score 55 · Answer 14 · 2022-08-21 16:58:47

55

Views

Is there a finite bound on the indexes of infinite retracts of an infinite virtually cyclic group $G$?

Published on 21 Aug 2022 - 16:58

score 247 · Answer 15 · 2022-08-24 19:05:41

247

Views

What would be some retracts of this graph?

Published on 24 Aug 2022 - 19:05

List Question

In general, how do you prove that a topological space isn’t a retraction of another?

Almost retracting a ball to its boundary

Showing there is a retraction from $\Bbb R^2$ to the closed disk $D$

Question about homotopy equivalence (Hatcher $0.4$)

Show that retraction is coequalizer.

Explicit retraction of $\mathbb{R}^n$ minus $k$ points to wedge sum of $k$ copies of $S^{(n-1)}$

Does finitely generated groups have finitely many finite retracts?

If $Y \subseteq Q$ is a retract of the Hilbert cube $Q$ and $Z \subseteq Q$ is homeomorphic to $Y$, is $Z$ a retract of $Q$?

$\Bbb{R}^3 - S^1$ deformation retracts to $S^2 \vee S^1$?

Fundamental group of the boundary of a torus with a point removed

Are there any topological spaces containing no proper retracts? i.e. $A\subset X$ s.t. $\exists r:X\to A$ continuous w/ $r(a)=a,\forall a\in A$

Does a free group $F$ of finite rank $n$ have finitely many retracts (as a subgroup)?

The number of retracts of $G\ltimes \mathbb{Z}$

Is there a finite bound on the indexes of infinite retracts of an infinite virtually cyclic group $G$?

What would be some retracts of this graph?

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