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nLab > Latest Changes: locally positive locale

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  1. Page created, but author did not leave any comments.

    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJun 1st 2022

    A “locally positive locale” is the same thing as an overt locale. This article is a duplicate.

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeJun 3rd 2022

    What shall we do? Delete the new page and create a redirect?

    I do think the existing page overt space is a bit confusing as a place for “overt locale” to redirect to, in that it tries to be very general about what constitutes a “space”, but someone looking for “overt locale” has a certain notion of space in mind already. It might be better to have a separate page called “open locale” which is just about the latter and is linked to by overt space. So one possibility would be to rename this new page to “overt locale” and move some stuff over from overt space.

    • CommentRowNumber4.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJun 3rd 2022

    Re #3: The only nonlocalic content of overt space is the sentence

    On the other hand, if ‘space’ means simply ‘set’, but ‘open’ refers to the synthetic notion induced by a dominance, then overtness of X is a nontrivial condition (and in fact, if all sets are overt in this sense then the dominance is trivial).

    Everything else involves topological spaces or locales.

    So perhaps it may be more appropriate to rename overt space to overt locale.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 4th 2022

    Sounds like all issues would be addressed by re-naming locally positive locale to overt locale and moving all locale-specific discussion to there.

  6. Added reference

    • Graham Manuell, Uniform locales and their constructive aspects, (arXiv:2106.00678)

    Anonymous

    diff, v2, current

  7. moving redirects for overt locale, overt locales, open locale, open locales from article on overt space

    Anonymous

    diff, v2, current

  8. adding a few other definitions of this notion of locale

    Anonymous

    diff, v2, current

    • CommentRowNumber9.
    • CommentAuthorTobyBartels
    • CommentTimeSep 13th 2024

    locally -1-connected

    diff, v5, current

1 to 9 of 9

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