We show that a two-dimensional (2D) spin-polarised Fermi gas
immersed in a 3D Bose-Einstein condensate (BEC) constitutes
a very promising system to realise a topological superfluid.
The fermions attract each other via an induced interaction
mediated by the bosons, and the resulting pairing is
analysed with retardation effects fully taken into account.
This is further combined with
Berezinskii-Kosterlitz-Thouless (BKT) theory to obtain
reliable results for the superfluid critical temperature. We
show that both the strength and the range of the induced
interaction can be tuned experimentally, which can be used
to make the critical temperature approach the maximum value
allowed by general BKT theory. Moreover, this is achieved
while keeping the Fermi-Bose interaction weak so that
three-body losses are small. We furthermore show that if the
fermions are confined in two layers, they can realise a
so-called Z_2 topological superfluid with time-reversal
symmetry and chiral edge states in analogy with the quantum
spin Hall state.