Topological higher-rank graphs and the $C^{\ast }$-algebras of topological 1-graphs

We introduce the notion of a topological higher-rank graph, a unified generalization of the higher-rank graph and the topological graph. Using groupoid techniques, we define the Toeplitz and Cuntz-Krieger algebras of topological higher-rank graphs, and show that the $C^{\ast }$-algebras defined are coherent with the existing theory.