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math.OA2021
Nowhere scattered C*-algebras
Hannes Thiel, Eduard Vilalta
We say that a C*-algebra is nowhere scattered if none of its quotients contains a minimal open projection. We characterize this property in various ways, by topological properties…
math.OA2021
Covering dimension of Cuntz semigroups II
Hannes Thiel, Eduard Vilalta
We show that the dimension of the Cuntz semigroup of a C*-algebra is determined by the dimensions of the Cuntz semigroups of its separable sub-C*-algebras. This allows us to remove…
math.OA2021
Covering dimension of Cuntz semigroups
Hannes Thiel, Eduard Vilalta
We introduce a notion of covering dimension for Cuntz semigroups of C*-algebras. This dimension is always bounded by the nuclear dimension of the C*-algebra, and for subhomogeneous…