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Journal of Operator Theory

Volume 78, Issue 1,  Summer  2017  pp. 89-117.

Composition of topological correspondences

Authors:  Rohit Dilip Holkar
Author institution: Department of Mathematics, Federal University of Santa Catarina, Florianopolis, 88. 040-900, Brazil and Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, NCL Colony, Pashan, Pune 411008, India

Summary:  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.

DOI: http://dx.doi.org/10.7900/jot.2016may30.2129
Keywords:  topological correspondences, composition of topological correspondences, functoriality of topological correspondences

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