A class of \(C^*\)-algebras generalizing both graph algebras and homeomorphism \(C^*\)-algebras IV, pure infiniteness

Abstract

This is the final one in the series of papers where we introduce and study the \(C^*\)-algebras associated with topological graphs. In this paper, we get a sufficient condition on topological graphs so that the associated \(C^*\)-algebras are simple and purely infinite. Using this result, we give one method to construct all Kirchberg algebras as \(C^*\)-algebras associated with topological graphs.