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nLab > Latest Changes: discrete and codiscrete topology

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  1.  
    • 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 Preorder→SetPreorder \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

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