Talk:Alexandroff topology

message: I have rearranged the history a bit and mentioned the usage in physics. I have also started sections on usage in comp sci and physics. I see that in physics papers the spelling "Alexandrov" is preferred. So maybe we should move back. 8 Oct 2004
I just checked my Johnstone and you are right, on p. 45 he uses "Alexandrov topology" for the T0 poset case. Interesting since Arenas seems to think that he is the first to talk about "Alexandroff topology" and from what I can make out the current usage of "Alexandroff topology" amongst the logic guys stems from Arenas' paper. The papers that use "Alexandroff topology" seem to be completely unaware of the categorical topology work on these spaces in the 80s under the name "finitely generated spaces" although the categorical topologists have picked up on their relevance to computer science, while still sticking to the name "finitely generated." There is also inconsistent usage of "upper topology" for this although the specialization (pre)order article uses "upper topology" for the coarsest topology consistent with the specialization preorder.
Ok how do we resolve the spelling issue, I agree that "Alexandrov" is the normal modern spelling of the name and it indeed appears as such in Johnstone, and as you say in denotational semantics work, but there is a whole lot more literature out there that spell this particular dude's name "Alexandroff". What should be said in the history section about Johnstone's use of "Alexandrov spaces" for the T0 poset case as opposed to Arenas' usage of "Alexandroff spaces" for general case? What should be said in the article Pavel Sergeevich Alexandrov about the spelling of the name?
:It should be enough to mention that it was romanised as -off in older papers - I doubt there was a standard system used in the 1930s. Charles Matthews
::The problem is that it is not simply older papers, there is a lot of current books and publications that spell the name "Alexandroff", remember his contribution to topology is much more than the Alexandroff/ov topology which is in fact extremely minor compared to his other work. - 8 Oct 2004
:Well OK - we need only set up a few redirects using the -off spelling. Charles Matthews
Regarding the history section, when you say the usage goes back beyond the 90's I take it you mean in connection with denotational semantics, since as it mentions they go back to 1937? Well Alexandroff-like topologies have been used since Scott's work in the early 70's? but as far as I'm aware they fell short of being the general Alexandroff topology. A reference for first usage in denotational semantics of these spaces is indeed needed for the article. So is a reference for the first discussion of these spaces in categorical topology, in particular who was actually responsible for noticing that they are the finitely generated objects in the category Top and what was the paper?
- 8 Oct 2004
Well, the page has been moved - I'm not convinced, and 'Alexandrov' is in Johnstone, Stone Spaces (1982), which is the standard reference. Also the denotational semantics literature quite generally uses the -ov version. The use of the topology also surely goes back beyond the 1990s.
Charles Matthews 17:01, 7 Oct 2004 (UTC)