Timeline for "Zorn's Lemma guarantees that all algebraic frames are spatial." Why?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 25, 2019 at 14:52 | comment | added | Zhenchao Lyu | Every distributive continuous lattice is a spatial frame. See "The spectral theory of distributive continuous lattices", Karl H. Hofmann and Jimmie D. Lawson 1978. | |
| Jan 24, 2016 at 9:32 | vote | accept | Anschel Schaffer-Cohen | ||
| Jan 22, 2016 at 10:17 | answer | added | Dominic van der Zypen | timeline score: 1 | |
| Dec 17, 2015 at 19:57 | comment | added | მამუკა ჯიბლაძე | I am not aware of any. If you have access to "Continuous Lattices and Domains" by Gierz, Hofmann, Keimel, Lawson, Mislove and Scott, there on page 126 is Theorem I-4.25 stating that for any $x\not\leqslant y$ in a bounded complete algebraic domain there is a completely irreducible element $p$ with $x\not\leqslant p$ and $y\leqslant p$. | |
| Dec 17, 2015 at 18:11 | comment | added | Anschel Schaffer-Cohen | I don't have access to that book out in the sticks unfortunately. Is there a sketch of the proof available online? | |
| Dec 15, 2015 at 21:25 | comment | added | მამუკა ჯიბლაძე | More generally (under AC) any continuous frame is spatial - see e. g. VII.4.3 in Johnstone's "Stone Spaces" (pp. 310-311) | |
| Dec 15, 2015 at 19:51 | history | asked | Anschel Schaffer-Cohen | CC BY-SA 3.0 |