Restricted product
|
|
The restricted product is a construction in the theory of topological groups.
Let <math> (G_1, K_1), (G_2, K_2) ,(G_3,K_3), ... <math> be a sequence of locally compact groups together with compact subgroups <math> K_i \subset G_i<math>. The restricted product
- <math> {\prod_i}' G_i\, <math>
is the set of sequences <math> (g_1, g_2, ...) <math> such that <math> g_i \in K_i <math> for all but finitely many <math> i<math>. The restricted product is itself a locally compact group. The best known example of this construction is that of the adele ring and idele group of an algebraic number field.