Timeline for Gossip about Grothendieck and distributive lattices
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 21, 2020 at 21:53 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Sep 20, 2010 at 22:12 | comment | added | Justin Hilburn | @Mark: In Indiscrete Thoughts Rota was referring to pointless topology which is the subject of Stone Spaces. | |
| Sep 19, 2010 at 23:44 | comment | added | Harry Gindi | @Mark: Ah, okay. WRT Johnstone's book, no, I haven't. | |
| Sep 19, 2010 at 19:32 | comment | added | user6976 | @Harry: I only repeated what Johnstone wrote in the introduction of his book. It seems to be different from what Rota had in mind. Did you read Johnstone's book? | |
| Sep 19, 2010 at 19:10 | comment | added | Harry Gindi | That is, if one wants to claim that the Zariski topology is a derivative of the Stone topology, one should look back to the papers of Zariski to understand the historical development better (and see if in fact the Zariski topology was developed from the stone topology). | |
| Sep 19, 2010 at 19:05 | comment | added | Harry Gindi | @Mark: The Zariski topology was invented substantially earlier by Zariski, not Grothendieck, for algebraic varieties and algebraic sets. It's more likely that Grothendieck noticed that since irreducible closed subsets are in canonical bijection with prime ideals, we can keep track of them as actual points. The fact that we can do this follows from the observation that while maximal ideals are not preserved under preimage, prime ideals are. This gives us an "enrichment" of the classical Zariski topology by adding generic points. | |
| Sep 19, 2010 at 16:39 | comment | added | user6976 | @Justin: Thank you for the reference to Johnstone book. He writes that Zariski topology is a generalization of Stone topology, that Grothendieck most probably knew about Stone's work, implicitely used it, but did not refer to Stone. That is not quite what Rota claimed, as I understand. Am I correct? | |
| Sep 19, 2010 at 3:50 | history | answered | Justin Hilburn | CC BY-SA 2.5 |