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created discrete and codiscrete topology
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.
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?
Fixed. i made everything referring specifically to topological spaces redirect to discrete and codiscrete topology.
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
I seem to recall “chaotic preorder” stands for the right adjoint of the forgetful functor from $Preorder \to Set$, and perhaps elsewhere too. It seems a bit silly to call the indiscrete topology chaotic however, even though it is a right adjoint.
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.
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
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