Timeline for Cardinality of the set of functions commuting with $f:X\to X$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 2, 2017 at 1:31 | answer | added | user44191 | timeline score: 2 | |
| Jan 1, 2017 at 23:24 | comment | added | Harry Altman | So combining this fact and the answers and comments below: The minimum number is $2^{|X|}$ if $X$ is uncountable, $|X|$ if $X$ is countable and nonempty, and $1$ if $X$ is empty. | |
| Jan 1, 2017 at 3:29 | comment | added | user44191 | @SamHopkins It's true for finite $X$; the proof starts by checking it for $X$ "connected" as defined by Will Sawin's graph below, and then inducting on components of $X$ by using the fact that $xy \geq x + y$ if $x, y > 1$ if no component has one element, and using the "extra" map that maps everything to that one element if one does. | |
| Dec 31, 2016 at 8:56 | vote | accept | Dominic van der Zypen | ||
| Dec 30, 2016 at 16:07 | comment | added | Sam Hopkins | Is it false for finite $X$? | |
| Dec 30, 2016 at 16:00 | answer | added | Will Sawin | timeline score: 7 | |
| Dec 30, 2016 at 15:12 | answer | added | Goldstern | timeline score: 5 | |
| Dec 30, 2016 at 14:27 | answer | added | Stefan Mesken | timeline score: 8 | |
| Dec 30, 2016 at 11:01 | history | asked | Dominic van der Zypen | CC BY-SA 3.0 |