C*-Algebras over Topological Spaces: The Bootstrap Class

TL;DR

This paper explores the structure of C*-algebras over topological spaces, including non-Hausdorff cases, and introduces a bootstrap class analogue within this context, enhancing understanding of their classification.

Contribution

It defines and studies C*-algebras over topological spaces and introduces an analogue of the bootstrap class for finite spaces, expanding the theoretical framework.

Findings

Triangulated category structure on Kasparov theory over spaces

Definition of bootstrap class for C*-algebras over finite spaces

Insights into non-Hausdorff topological space cases

Abstract

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. We introduce and describe an analogue of the bootstrap class for C*-algebras over a finite topological space.