Hausdorff completion


In algebra, the Hausdorff completion of a group G with filtration is the inverse limit of the discrete group. A basic example is a profinite completion. The image of the canonical map is a Hausdorff topological group and its kernel is the intersection of all : i.e., the closure of the identity element. The canonical homomorphism is an isomorphism, where is a graded module associated to the filtration.
The concept is named after Felix Hausdorff.