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arXiv · 2103.13062

Covering dimension of Cuntz semigroups II

Hannes Thiel·Eduard Vilalta
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Abstract

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 separability assumptions from previous results on the dimension of Cuntz semigroups. To obtain these results, we introduce a notion of approximation for abstract Cuntz semigroups that is compatible with the approximation of a C*-algebra by sub-C*-algebras. We show that many properties for Cuntz semigroups are preserved by approximation and satisfy a L\"owenheim-Skolem condition.

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Hannes Thiel, Eduard Vilalta. 2021-03-24. Covering dimension of Cuntz semigroups II. https://arxiv.org/abs/2103.13062

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