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 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 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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).

nLab > Latest Changes: point-free topology

Bottom of Page

1 to 14 of 14

  1.  

  1. Writing up “point-free” means points are models of a geometric theory.

    Steve Vickers

    diff, v10, current

  2. More on point-free spaces and geometric theories.

    Steve Vickers

    diff, v12, current

  3. Pointwise reasoning for point-free spaces.

    Steve Vickers

    diff, v13, current

  4. Start on a section on point-free bundles

    Steve Vickers

    diff, v13, current

  5. Finished first stab at section on bundles.

    Steve Vickers

    diff, v14, current

  6. Section on sets of points of point-free spaces, with an illustrative example.

    Steve Vickers

    diff, v15, current

  7. Deleted previous definition of pointwise/pointless.

    It made a valid categorical point about the terminal object being a generator, but said nothing significant about what it takes to give a formulation of topology.

    Steve Vickers

    diff, v15, current

    • CommentRowNumber8.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 27th 2018

    Steve, first of all: welcome! I think it’s great that you are getting interested in sharing your insights on the nLab, and the influx of energy is very welcome.

    Normally, when it comes to deleting another person’s work (I don’t mean typos or other careless errors), we have a little discussion at the nForum beforehand. Maybe the author of the text would like to clarify, have another crack at it, etc. – but once someone else begins writing over it, this becomes more awkward to do.

    I don’t have much of an opinion about this particular case, but I just wanted you to know about the “etiquette” (for lack of a better word) that has developed over time at the nLab. A rule of thumb is to feel free to add, but be circumspect and diplomatic about subtracting (I’m reminded here of the “Yes, and…” precept of improv comedy). My own sense is that the success of the nLab wiki depends on this type of communication.

    • CommentRowNumber9.
    • CommentAuthorMike Shulman
    • CommentTimeNov 27th 2018

    Agreed! However, in this case I do think that something should be preserved of the previous text. I don’t think that this definition was ever intended to say “what it takes to give a formulation of topology”, so I don’t think it makes sense to criticize or delete it for failing to do so. Perhaps it pretended to a little undeserved formality, but I think the “valid categorical point” should be kept.

    • CommentRowNumber10.
    • CommentAuthorMike Shulman
    • CommentTimeNov 27th 2018

    Restored earlier “definition” of pointlessness in a subsection of Examples/Definition, with caveats and with definition environment removed to make it feel less official.

    diff, v16, current

    • CommentRowNumber11.
    • CommentAuthorstevevickers
    • CommentTimeNov 29th 2018
    Apologies - I mentioned it to Urs, because he emailed me spontaneously, and he said "Go ahead". But I never checked with Toby. I suppose the correct channel is via nForum. How long do you typically allow for responses?

    Of course, I'd also be very pleased to see comments on the mathematics and what readers need to see in the presentation. Although it is one small page, I'm trying to seed a conversation about how key intuitions such as "generalized space" and "relativization" (bundle) can be exposed in definitions and results that might otherwise be impenetrably technical.
    • CommentRowNumber12.
    • CommentAuthorMike Shulman
    • CommentTimeNov 29th 2018

    I don’t think there’s a fixed time to wait; a few days to a week is probably fine. Of course someone who was away or busy at that time may come back later and reopen the question of restoring the deleted material (since nothing should ever be permanently lost on a wiki), but asking before deleting sends a signal of politeness and respect.

    Your proposed conversation sounds really interesting, though unfortunately I haven’t had the time yet to read carefully through your additions.

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeJan 17th 2023

    added pointer to:

    diff, v17, current

    • CommentRowNumber14.
    • CommentAuthorGuest
    • CommentTimeMay 23rd 2023

    removed duplicate redirect for pointless topology

    diff, v18, current

1 to 14 of 14

  1.