Call
In mathematics, the restricted product is a construction in the theory of topological groups.
Let I {\displaystyle I} be an index set; S {\displaystyle S} a finite subset of I {\displaystyle I}. If G i {\displaystyle G_{i}} is a locally compact group for each i ∈ I {\displaystyle i\in I} , and K i ⊂ G i {\displaystyle K_{i}\subset G_{i}} is an open compact subgroup for each i ∈ I ∖ S {\displaystyle i\in I\setminus S} , then the restricted product
is the subset of the product of the G i {\displaystyle G_{i}} 's consisting of all elements i ∈ I {\displaystyle _{i\in I}} such that g i ∈ K i {\displaystyle g_{i}\in K_{i}} for all but finitely many i ∈ I ∖ S {\displaystyle i\in I\setminus S}.
This group is given the topology whose basis of open sets are those of the form