Goerke, Gavin2023-04-272023-04-2720232023-04-27http://hdl.handle.net/1828/15010In this thesis we study the ideal intersection property for inclusions of C*-algebras C*(H)↪C*(G) induced from a family of open subgroupoids {H} of a locally compact Hausdorff étale groupoid G. For such a family of open subgroupoids we define the notion of relative topological principality and we show that if G is relatively topologically principal to {H} then a representation of C*(G) is faithful if and only if the restriction of the representation to each of the subalgebras C*(H) is faithful. This gives a new method of verifying injectivity of representations of reduced groupoid C*-algebras. As an application of our result we prove a uniqueness theorem for C*-algebras of left cancellative small categories which generalizes a theorem of Marcelo Laca and Camila Sehnem for Toeplitz algebras of group embeddable monoids.enAvailable to the World Wide WebC*-algebrasgroupoidtopologically freeThesis