- Abstract. Let Γ be a hyperbolic group. The normal topology on Γ is defined by taking all cosets of infinite normal subgroups as a basis. This topology is finer than the pro-finite topology, but it is not discrete. We prove that every quasiconvex subgroup∆< Γ is closed in the normal topology. For a uniform lattice Γ< PSL2 (C) we prove, using the tameness theorem of Agol and Calegary-Gabai, that every finitely generated subgroup of Γ is closed in the normal topology.