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We study Sims-Yeend's product system C*-algebras and topological higher-rankgraph C*-algebras by Yeend. We give a relation between Katsura's Cuntz-Pimsnercovariance and Sims-Yeend's one by a direct approach and an explicit form ofthe core of product system C*-algebras. Finally, we prove Cuntz-Krieger typeuniqueness theorem for topological higher-rank graph C*-algebras under certainaperiodic condition.

Cuntz-Krieger type uniqueness theorem for topological higher-rank graph C*-algebras