Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Covering dimension of Cuntz semigroups II   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.

16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org