Timeline for Nonequivalent definitions in Mathematics
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 25, 2019 at 16:45 | comment | added | LSpice | The question about connectedness of the empty set is the question of whether the set of components of the empty set is $\emptyset$ or $\{\emptyset\}$. (Fortunately, according to my Discrete Mathematics students, there is no difference between these two sets.) | |
| Apr 28, 2018 at 11:38 | comment | added | Jarek Kuben | This has been discussed on MO before. | |
| Nov 24, 2017 at 11:54 | comment | added | Carsten S | The empty space is connected, but it is not $0$-connected. (Of course it is not even $(-1)$-connected, that is the point.) | |
| Nov 24, 2017 at 8:18 | comment | added | Goldstern | @LukasLewark If you view the decomposition into connected components as a partition (i.e., a set of nonempty equivalence classes), then it is truly unique, not unique up to permutations. | |
| Nov 23, 2017 at 14:49 | comment | added | Jeff Strom | This mini-debate is exactly the simply-connected+(conntected or not) debate one dimension down! | |
| Nov 23, 2017 at 10:50 | comment | added | Duchamp Gérard H. E. | @LukasLewark I agree ... connected components are seen as "atoms" and therefore empty space should not be considered connected although this does not match with the formal definition. | |
| Nov 23, 2017 at 5:41 | comment | added | Lukas Lewark | The empty space should not be seen as connected, for the same reason as units in a ring are not primes: you want the decomposition into connected components to be unique up to permutation. I'm sure others will disagree, though, so it's another good example :) | |
| Nov 23, 2017 at 3:11 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Nov 22, 2017 at 22:16 | comment | added | Mike Shulman | For that matter, is the empty space connected? | |
| Nov 22, 2017 at 22:12 | history | answered | Duchamp Gérard H. E. | CC BY-SA 3.0 |