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.
References
- Nicolas Bourbaki, Commutative algebra
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