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    • CommentRowNumber1.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJul 25th 2019

    Added some criteria for spatiality.

    diff, v8, current

    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTime7 days ago

    Exactly where in the literature does the term “topological locale” occur?

    Johnstone (Stone Spaces, Sketches of the Elephant) and Picado-Pultr both use “spatial locale”, and “topological locale” is never mentioned in their books at all.

    diff, v9, current

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTime7 days ago

    Don’t recall ever seeing it. Probably should be renamed “spatial locale”.

    • CommentRowNumber4.
    • CommentAuthorDmitri Pavlov
    • CommentTime7 days ago

    Renamed. Preserved the redirects.

    diff, v10, current

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTime5 days ago

    Hang on, I think there was a reason for calling it “topological locale” even if that term doesn’t appear elsewhere in the literature. The point is that according to a broad perspective, a locale is itself already a kind of space. The term “spatial locale” assumes that “space” means “topological space”, but that’s often an unwarranted assumption.

    • CommentRowNumber6.
    • CommentAuthorTodd_Trimble
    • CommentTime5 days ago

    Are you saying it should be titled “topological locale” after all?

    As far as I know, there is never any question that “spatial locale” means “topological spatial locale” – that’s how everyone uses the term – so how could it be an unwarranted assumption?

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTime5 days ago

    I’m not saying there’s potential confusion in practice, just that the term clashes with our general use of space on the nLab. The previous discussion is here. I’m fine with renaming the page (though Toby might object), but it might be worth adding a remark on terminology.

    • CommentRowNumber8.
    • CommentAuthorDmitri Pavlov
    • CommentTime5 days ago
    • (edited 5 days ago)

    We already have a whole section on terminology in the article.

    “Topological X” very consistently refers to an X-object in the category of topological spaces. Topological group, topological ring, topological vector space. Frames are also algebraic structures.

    Also, “topological locale” suggests that these particular locales have more to do with topology or topological spaces than the other locales, which is not true.

    I agree that “spatial locale” is bad terminology and something like “pointful locale” or “sober locale” (but definitely not “topological locale”) would be much better.

    However, I would very strongly argue that nLab should stick to established terminology where it exists and not use some made-up terms, since the latter make it very difficult to follow up with a literature search after reading some nLab article.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTime5 days ago

    The term “locale with enough points” would match the terminology and intent used in the entry and is used in standard texts as well as in current discussion (according to a quick Google search)

    • CommentRowNumber10.
    • CommentAuthorDmitri Pavlov
    • CommentTime5 days ago

    Re #9: Yes, and this term is already mentioned in the article. It is introduced by Johnstone in “Stone spaces”.

    • CommentRowNumber11.
    • CommentAuthorDmitri Pavlov
    • CommentTime5 days ago

    Deleted duplicate redirects.

    Why do “locale of opens” and “locale of open subspaces” redirect here?!

    diff, v11, current

    • CommentRowNumber12.
    • CommentAuthorDmitri Pavlov
    • CommentTime5 days ago

    Deleted duplicate redirects.

    Why do “locale of opens” and “locale of open subspaces” redirect here?!

    diff, v12, current

    • CommentRowNumber13.
    • CommentAuthorDmitri Pavlov
    • CommentTime5 days ago

    Deleted duplicate redirects.

    Why do “locale of opens” and “locale of open subspaces” redirect here?!

    diff, v13, current

    • CommentRowNumber14.
    • CommentAuthorMike Shulman
    • CommentTime5 days ago

    Why do “locale of opens” and “locale of open subspaces” redirect here?!

    See the old discussion I linked in #7.

    • CommentRowNumber15.
    • CommentAuthorMike Shulman
    • CommentTime5 days ago

    I like “locale with enough points” as a name for the page (with “spatial locale” mentioned prominently as a standard terminology at the top of the page, and of course as a redirect).

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