A class of C∗-algebras generalizing both graph algebras and homeomorphism C∗-algebras IV, pure infiniteness

AbstractThis 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