  A three-component Fermi gas near a broad Feshbach resonance does not have a
universal ground state due to the Thomas collapse, while it does near a narrow
Feshbach resonance. We explore its universal phase diagram in the plane of the
inverse scattering length 1/akF and the resonance range RkF. For a large RkF,
there exists a Lifshitz transition between superfluids with and without an
unpaired Fermi surface as a function of 1/akF. With decreasing RkF, the Fermi
surface coexisting with the superfluid can change smoothly from that of atoms
to trimers ("atom-trimer continuity"), corresponding to the quark-hadron
continuity in a dense nuclear matter. Eventually, there appears a finite window
in 1/akF where the superfluid is completely depleted by the trimer Fermi gas,
which gives rise to a pair of quantum critical points. The boundaries of these
three quantum phases are determined in regions where controlled analyses are
possible and are also evaluated based on a mean-field plus trimer model.
