Completion

The procedure of adjoining limits of Cauchy nets, sequences, or more general Cauchy filters to a metric, uniform, or algebraic object to obtain a complete object; common instances include Cauchy completion of metric spaces and I-adic completion of rings.

The process of adjoining limits of Cauchy sequences (or inverse‑limit points) with respect to a topology or filtration to obtain a complete object in which prescribed Cauchy nets converge.

The process of adjoining limits of Cauchy-like sequences (or inverse-limit elements determined by a filtration or topology) to an algebraic object so that the resulting object is complete with respect to the given topology or filtration.