  Suppose that all hyperbolic groups are residually finite. The following
statements follow: In relatively hyperbolic groups with peripheral structures
consisting of finitely generated nilpotent subgroups, quasiconvex subgroups are
separable; Geometrically finite subgroups of non-uniform lattices in rank one
symmetric spaces are separable; Kleinian groups are subgroup separable. We also
show that LERF for finite volume hyperbolic 3-manifolds would follow from LERF
for closed hyperbolic 3-manifolds.
  The method is to reduce, via combination and filling theorems, the
separability of a quasiconvex subgroup of a relatively hyperbolic group G to
the separability of a quasiconvex subgroup of a hyperbolic quotient G/N. A
result of Agol, Groves, and Manning is then applied.
