  We introduce a new `Thom class' formulation of topological T-duality for
principal torus bundles. This definition is equivalent to the established one
of Bunke, Rumpf, and Schick but has the virtue of removing the global
assumptions on the H-flux required in the old definition. With the new
definition, we provide easier and more transparent proofs of the classification
of T-duals and generalise the local formulation of T-duality for circle bundles
by Bunke, Schick, and Spitzweck to the torus case.
