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: preconvergence space

Bottom of Page

1 to 11 of 11

  1.  

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

    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 5th 2022

    I have adjusted wording and hyperlinking of the lead-in sentences, for readability.

    It would be good for the entry to cite some references.

    diff, v4, current

  3. Added the definition of preconvergence space directly in terms of nets without using filters

    Anonymouse

    diff, v6, current

  4. In the existing mathematical literature on topology and convergence, preconvergence spaces have an requirement that they satisfy the isotone condition; see i.e.

    • Dolecki, Szymon; Mynard, Frédéric (2016). Convergence Foundations Of Topology. New Jersey: World Scientific Publishing Company. ISBN 978-981-4571-52-4. OCLC 945169917.

    • Dolecki, Szymon (2009). Mynard, Frédéric; Pearl, Elliott (eds.). “An initiation into convergence theory”. Beyond Topology. Contemporary Mathematics Series A.M.S. 486: 115–162. (pdf)

    Are there any references which use “preconvergence space” for this space without the isotone condition?

  5. In Non-symmetric Convenient Topology and its Relation to Convenient Topology the author Gerhard Preuss defines a “preconvergence space” to be this other structure:

    • a preconvergence space is a preuniform convergence space which is ‘generated’ by its preconvergent filters

    which doesn’t have anything to do with the other definition by Dolecki and Mynard etc.

    See also,

  6. John Baez suggested that I add these references to the article even though none of the definitions of a preconvergence space found in the articles are the same as the definition already given in the article.

    diff, v8, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTime2 days ago

    Madeleine, I am not sure what you are trying to do (or what somebody else is making you do), but if the entry needs fixing there is no need to hesitate: After all, this is one of the notorious Anonymous edits — you know the story.

    The first thing I asked (in #2) when the entry was anonymously created, in 2002, is for references supporting its claims. As usual, this request was ignored by the entry’s author.

    It sounds now like you have the references and that they disagree with our notorious anonymous contributor. If so, by all means, let’s fix whatever needs fixing.

  8. I went ahead and edited the article with a correct definition of preconvergence spaces.

    diff, v9, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTime2 days ago

    Good, thanks!

    • CommentRowNumber10.
    • CommentAuthorJohn Baez
    • CommentTime2 days ago
    • (edited 2 days ago)

    By the way, I didn’t “make” Madeleine do anything. She came up with a bunch of references for “preconvergence space” but was worried because the definition used in those references did not match the definition given on the nLab. I suggested that she take suitable actions to improve the situation after consulting the nForum. I’m glad she did.

  11. Sorry for the bad wording on my part.

1 to 11 of 11

  1.