Timeline for Nonhomeomophic spaces with homeomorphic mapping cones
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 26, 2020 at 14:19 | comment | added | Jeremy Brazas | Another example to describe the same phenomenon: a graph with two vertices $a,b$, infinitely many edges connecting $a$ and $b$, plus infinitely many edges connected just to $a$ should do also the trick if $A=\{a\}$ and $B=\{a,b\}$ with $\alpha,\beta$ inclusions. | |
| Aug 26, 2020 at 3:01 | comment | added | Andreas Blass | @JeffStrom Oops, you're right. Start with infinitely many whiskers and infinitely many loops (or arches). That seems to fix the problem. | |
| Aug 26, 2020 at 3:00 | comment | added | Jeff Strom | How about instead a line with semicircles joining $0$ (the basepoint) to $n$ for $n\in \mathbb{N}$. Then attaching a cone on a finite set does not change the homeomorphism type. | |
| Aug 26, 2020 at 2:58 | comment | added | Jeff Strom | But adding the cone on $B$ will make a closed loop, right? But this seems a promising approach. | |
| Aug 26, 2020 at 2:29 | history | answered | Andreas Blass | CC BY-SA 4.0 |