Talk:Dyadic rational

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[edit] Ring properties

The question about ring properties: better dealt with on the localization of a ring page?

The question certainly does not belong in the article so I have deleted what properties does this ring have?. --Henrygb 23:09, 30 Apr 2005 (UTC)

[edit] Dyadic solenoid

I have added stuff about the dyadic solenoid as fitting well here, but I'm somewhat unclear about a couple of points. On the general level, Pontryagin duality interchanging direct and inverse limits: this would be OK, but I guess there is a point here, namely that the dyadic rationals must be taken with the discrete topology, and certainly not as a subspace of the real line. Also, the inverse limit could be taken either as indexed by N, or bi-infinite.

Charles Matthews 11:14, 13 Sep 2004 (UTC)

[edit] Solenoid redux

I believe that the dyadic solenoid is also a fiber bundle over a circle, with fiber that is a Cantor set. (Right?) However, the right way to write the the covering is a bit confusing.

Also, this article states the dyadic solenoid is a topological group, but the group action is a bit mysterious to me: is it really a group, or is it a topological monoid ? linas 15:08, 19 October 2005 (UTC)

There is now a solenoid group page, to which I have linked; these things are really too advanced to go on a dyadic rational page. Charles Matthews 15:14, 19 October 2005 (UTC)
If you run across references, I'd appreciate that; w/clarification of relationship to Dirichlet characters as well, and relationship to Dirichlet L-functions.linas 01:44, 20 October 2005 (UTC)
What relationship? I suppose in a sense Hecke characters might be linked, but Dirichlet characters are fundamentally just on a compact group (product of p-adic units over all p). Charles Matthews 08:28, 20 October 2005 (UTC)
Errm, I don't know. For a moment there, I had this glimpse. I'm working on it. linas 00:41, 21 October 2005 (UTC)