Timeline for Whether an isotone bijection from a power set lattice to another sends singletons to singletons
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Aug 4 at 17:28 | comment | added | Salvo Tringali | @Keith In the proof of their 2nd claim, David Gao is using that $f(a \land b) \leq f(a) \land f(b)$, not that $f(a \land b) = f(a) \land f(b)$. This follows from $f$ being isotonic, plus the fact that $a \land b \leq a$ and $a \land b \leq b$. | |
| Aug 4 at 17:19 | comment | added | Keith | How do we know that our isotone bijection preserves meets? This is required to be a boolean algebra morphism and you use this fact in your proof of the claim that it preserves compliments. I suspect I'm just missing something but this proof doesn't make sense to me. | |
| Aug 4 at 12:20 | vote | accept | Salvo Tringali | ||
| Aug 4 at 10:46 | comment | added | Emil Jeřábek | You can change which answer is accepted, it’s not a once and for all thing. I think his answer deserves it more. But anyway, it’s up to you. | |
| Aug 4 at 10:14 | comment | added | Emil Jeřábek | @SalvoTringali IMHO you should accept the best answer, not the first one. | |
| Aug 4 at 8:59 | comment | added | Salvo Tringali | +1. I am accepting Emil Jeřábek's answer since it came first. However, I like this answer even more: it makes the proof neater and demonstrates that, after all, power set lattices are not that special with respect to the question raised in the OP. | |
| Aug 4 at 8:03 | history | answered | David Gao | CC BY-SA 4.0 |