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Apr 12, 2019 at 2:14 comment added Robert Furber @DenisNardin These things are what I know as Priestley spaces: en.wikipedia.org/wiki/Priestley_space
Apr 11, 2019 at 18:34 vote accept CommunityBot
Apr 11, 2019 at 18:20 comment added Denis Nardin What is true is that the category of spectral spaces is equivalent to the category of posets in Stone spaces (i.e. totally disconnected, compact Hausdorff spaces), so in a sense the spectrum is only the datum of the underlying Stone space and of the specialization order. However I don't think this is a fruitful avenue
Apr 11, 2019 at 18:11 history answered Tim Campion CC BY-SA 4.0