Composition of topological correspondences

Abstract

In our previous work, \textit{J. Operator Theory}, \textbf{77}(2017), 217--241, we define a topological correspondence from a locally compact groupoid equipped with a Haar system to another one and we show that a topological correspondence, (X,λ), from a locally compact groupoid with a Haar system (G,α) to another one, (H,β),produces a C∗-correspondence H(X) from C∗(G,α) to C∗(H,β) . In the present article, we describe how to form a composite of two topological correspondences when the bispaces are Hausdorff and second countable in addition to being locally compact.