A completion for partially ordered Abelian groups (Q794682)

The author describes a completion process for a partially ordered abelian group G, using non-empty subsets of G which are bounded above and closed in the Scott topology on G. This completion is compared with the more familiar Dedekind completion. The author's completion satisfies a universal property which makes it a left adjoint to the forgetful functor from the category of partially ordered abelian groups with order preserving (or reversing) Scott continuous group homomorphisms to the category of semicontinuous closed posets with semicontinuous functions.