Timeline for Snake-like continua and universal images
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 4, 2016 at 7:54 | comment | added | Lasse Rempe | @WłodzimierzHolsztyński - no, Logan's example is far from simple (as you might expect, given how long the problem had been open). It is a limit of simple triods, each very close to the previous one in Hausdorff distance, but wrapped around it in such a way that the span of these triods tends to zero. However, they are carefully constructed so that no chain of a certain definite mesh covers any of these continua. This is already a strenghtening of known results; more work is then required to see that the limit itself is not chainable. I cannot say that I have digested all the details. | |
| May 4, 2016 at 4:41 | vote | accept | Włodzimierz Holsztyński | ||
| May 4, 2016 at 4:41 | comment | added | Włodzimierz Holsztyński | Lasse, super! Thank you. I am slow, so sorry. (It'd be nice to have an idea of Logan Hoehn's example; I don't expect anything simple though). | |
| May 3, 2016 at 12:27 | comment | added | Vincent | Speaking of self contained, would you might retelling the Erdos story here? | |
| May 3, 2016 at 11:01 | comment | added | Lasse Rempe | I enjoy thinking about these concepts and problems, so I have added a detailed explanation - I hope this helps. However, in general, I feel that - while more detailed answers are always nice, and likely to help more people - it is enough if a MO answer gives the relevant information and references to definitions and further background. Certainly if I think a question is worth asking on MO, I also think it is worth the effort of reading up on any material mentioned in answers. | |
| May 3, 2016 at 10:56 | history | edited | Lasse Rempe | CC BY-SA 3.0 |
Added update provided by Logan Hoehn
|
| Apr 30, 2016 at 19:38 | history | edited | Lasse Rempe | CC BY-SA 3.0 |
Provided definitions and details.
|
| Apr 30, 2016 at 13:50 | comment | added | Włodzimierz Holsztyński | I'd appreciate it. People are different :-). I read the respective definitions a few times in my life (years ago). And I worked on somewhat related problems. Nevertheless, I have never mastered those definitions. They are perhaps even less known to non-specialists while these topics have a universal appeal (I'd think). Let's remember the remarkable story of Paul Erdos and his under-additive 1-dim example. | |
| Apr 30, 2016 at 13:38 | comment | added | Lasse Rempe | The concepts of span and semispan - which are classical and well established, though admittedly somewhat specialised - can be found in the references provided. I think for an answer, as opposed to a question, that should be sufficient, but I will add some details when I get the chance. | |
| Apr 30, 2016 at 2:08 | comment | added | Włodzimierz Holsztyński | My general comment addressed to the whole MO: let's make MO posts more self-contained, let them include explicit definitions. | |
| Apr 27, 2016 at 21:21 | history | edited | Lasse Rempe | CC BY-SA 3.0 |
removed incorrect example
|
| Apr 27, 2016 at 15:39 | history | answered | Lasse Rempe | CC BY-SA 3.0 |