Cartan Subalgebras of Topological Graph Algebras and k-Graph C*-algebras

In this paper, two sufficient and necessary conditions are given. The first one characterizes when the boundary path groupoid of a topological graph without singular vertices has closed interior of its isotropy group bundle, and the second one characterizes when the path groupoid of a row-finite k-graph without sources has closed interior of its isotropy group bundle. It follows that the associated topological graph algebra and the associated k-graph C*-algebra have Cartan subalgebras due to a result of Brown-Nagy-Reznikoff-Sims-Williams.