A revised augmented Cuntz semigroup

We revise the construction of augmented Cuntz semigroup functor used by first author to classify inductive limits $1$-dimensional noncommutative CW complexes. The original has good functorial properties when restricted class C*-algebras stable rank one. proposed here for all C*-algebras: we show that is a stable, continuous, split exact functor, from category Cu-semigroups.