Timeline for Completion of the rationals to the reals as an inverse limit construction?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Apr 1, 2010 at 4:42 | comment | added | S. Carnahan♦ | Now that I'm thinking a little more about it, the maximal ideal is not closed, and this produces a strange topology on the "residue field" (namely, 0 is dense in {-1,0,1}). | |
| Apr 1, 2010 at 4:38 | comment | added | S. Carnahan♦ | @François: A quotient of a (topological) commutative monoid M is constructed using a (closed) congruence relation, which is a (closed) equivalence relation invariant as a subset of $M \times M$ under translation by the diagonal action of M. Given a closed ideal I, the subset $I \times I$ forms a closed congruence relation. In particular, the ideals I described above should not have had strict inequalities. | |
| Apr 1, 2010 at 4:30 | comment | added | S. Carnahan♦ | @Pete: It is quite possible that no one actually calls it by that name, but lots of people say that other people call it that. I heard the term from Kiran Kedlaya (who seemed to be passing on what he had heard elsewhere), but there are close variants in print. For example, Durov calls it the completed local ring at infinity in his massive tome on Arakelov geometry, where it has a bit more structure than a monoid. | |
| Mar 30, 2010 at 21:07 | comment | added | Pete L. Clark | Who calls $[-1,1]$ the "ring of integers of $\mathbb{R}$"? I want to have a talk with them. It's not a ring, and it doesn't contain the integers! | |
| Mar 30, 2010 at 19:12 | comment | added | François G. Dorais | I probably tried to do something silly and completely different from what you have in mind, but I don't see how to compute the quotients in the third paragraph. | |
| Mar 30, 2010 at 19:02 | history | edited | S. Carnahan♦ | CC BY-SA 2.5 |
added 8 characters in body
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| Mar 30, 2010 at 18:57 | history | answered | S. Carnahan♦ | CC BY-SA 2.5 |