Profinite topology

Definition
The profinite topology on a group is a topology on the underlying set of the group defined in the following equivalent ways:


 * 1) It has as a basis of open subsets all left cosets of subgroups of finite index.
 * 2) It has as a basis of open subsets all right cosets of subgroups of finite index.
 * 3) It has as a basis of open subsets all cosets of normal subgroups of finite index.

Under the profinite topology, any group becomes a topological group.