Abstract
AbstractWe 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 $\operatorname {\mathrm {Lsc}} (X,\overline {\mathbb {N}})$ for some $T_1$ -space X. In our investigations, we also uncover new properties that the Cuntz semigroup of all AI-algebras satisfies.
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