Not signed in (Sign In)

Start a new discussion

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-categories 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry goodwillie-calculus graph graphs gravity grothendieck 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 infinity integration integration-theory k-theory lie lie-theory limit limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monads monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories nonassociative noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory 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 string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory 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).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 13th 2010
    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeOct 13th 2010
    Though the terminology codiscrete may be better and is in some use among category theorists, among other mathematicians the other two terms seem to be much more common (indiscrete and trivial). (I am not complaining, just noting.)
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 13th 2010

    Yes, right. I did mention these terms, though. But I think here we may play Bourbaki a bit. I am really paving the way for a comprehensive discussion of discrete and codiscrete spaces at cohesive topos.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeOct 13th 2010
    I am sure you are going to describe a magnificent picture...just go on nondistracted :)

    I am giving a talk in Vienna on a different topic (key words: Lie algebroids, Leibniz algebras, symmetrization maps, realizations and deformation quantization). I am a bit at the edge of getting sick before the travel. Need some rest before...
    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeOct 14th 2010

    I observe that discrete topology redirects to discrete space, but codiscrete topology redirects to discrete and codiscrete topology. Probably either the first should redirect to discrete and codiscrete topology or the second should redirect to codiscrete space?

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeOct 14th 2010

    Fixed. i made everything referring specifically to topological spaces redirect to discrete and codiscrete topology.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeMay 21st 2019

    added mentioning of the alternative name “chaotic topology” for “indiscrete topology”, and pointer to places that use it (so far: Stacks Projcect 7.6.6, but eventually there should be more canonical pointers)

    Incidentally, the Wikipedia entry on Grothendieck topologies currently mixes up the terminology here. Somebody should fix this

    diff, v7, current

    • CommentRowNumber8.
    • CommentAuthorAli Caglayan
    • CommentTimeMay 26th 2019

    I seem to recall “chaotic preorder” stands for the right adjoint of the forgetful functor from PreorderSetPreorder \to Set, and perhaps elsewhere too. It seems a bit silly to call the indiscrete topology chaotic however, even though it is a right adjoint.

    • CommentRowNumber9.
    • CommentAuthorTodd_Trimble
    • CommentTimeMay 26th 2019

    I’m not sure who introduced the term; might it have been Lawvere? Here is one source of discussion: Lawvere.

    In a footnote here, page 3, completely random motion (chaos) is opposed to immobility (discreteness), where open sets cannot distinguish between point-particles in motion in the chaotic case.

    Google searches confirm that the terminology continues to be used to this day, so the nLab should keep the terminology on record.

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeMay 27th 2019
    • (edited May 27th 2019)

    added the pointer to Lawvere’s “Functorial remarks on the general concept of chaos”, and am also adding it at codiscrete space and at chaos

    diff, v9, current

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)