Completions of topological Abelianp-groups

Abstract

In the study of an Abelian group a useful method is the consideration of its completions with respect to various topologies, e.g. the p-adic topology. Within a certain class of topologies, defined in terms of families of preradicals and including the p-adic topology, it is shown that even in the non-Hausdorff case Completions do exist (although the uniqueness is lost). It is shown that every Abelian p-group of countable length is embeddable as an isotype subgroup of a fully complete Abelian group of the same length. Examples of the non-uniqueness of completions are also given.