Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
  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.

  2. Added reference

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

    Anonymous

    diff, v2, current

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

    Anonymous

    diff, v2, current

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

    Anonymous

    diff, v2, current