  We provide an abstract characterization for the Cuntz semigroup of unital
commutative AI-algebras, as well as a characterization for abstract Cuntz
semigroups of the form $\text{Lsc} (X,\overline{\mathbb{N}})$ for some
$T_1$-space $X$. In our investigations, we also uncover new properties that the
Cuntz semigroup of all AI-algebras satisfies.

Operator Algebras