Cuntz’s ax+b-Semigroup C*-Algebra Over ℕ and Product System C*-Algebras

We investigate C*-algebras associated with row-finite topological higher-rank graphs with no source, which are based on product system C*-algebras. We prove the Cuntz-Krieger uniqueness theorem, and provide the condition of simplicity and purely infiniteness of our algebras. We give examples of non-discrete topological higher-rank graphs whose C*-algebras contain Cuntz’s ax+b-semigroup C*-algebra over ℕ.