Isomorphisms of tensor algebras of topological graphs Kenneth DavidsonJean Roydor 47L5547L40topological graphC*-correspondencepiecewise conjugate We show that if two tensor algebras of topological graphs are algebraically isomorphic, then the graphs are locally conjugate. Conversely, if the base space is at most one-dimensional and the edge space is compact, then locally conjugate topological graphs yield completely isometrically isomorphic tensor algebras. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4816 10.1512/iumj.2011.60.4816 en Indiana Univ. Math. J. 60 (2011) 1249 - 1266 state-of-the-art mathematics http://iumj.org/access/