In mathematics, the restricted product is a construction in the theory of topological groups. Let be an index set; a finite subset of . If is a locally compact group for each , and is an open compact subgroup for each , then the restricted product is the subset of the product of the 's consisting of all elements such that for all but finitely many . This group is given the topology whose basis of open sets are those of the form where is open in and for all but finitely many . One can easily prove that 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 a global field. See also Direct sum References Topological groups