\(C^*\)-algebras over topological spaces: the bootstrap class. (English) Zbl 1191.46058
Summary: We carefully define and study \(C^*\)-algebras over topological spaces, possibly non-Hausdorff, and review some relevant results from point-set topology along the way. We explain the triangulated category structure on the bivariant Kasparov theory over a topological space and study the analogue of the bootstrap class for \(C^*\)-algebras over a finite topological space.
MSC:
46L80 | \(K\)-theory and operator algebras (including cyclic theory) |
19K35 | Kasparov theory (\(KK\)-theory) |