A class of $C^{\ast }$-algebras generalizing both graph algebras and homeomorphism $C^{\ast }$-algebras IV, pure infiniteness

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