  We describe the on-going effort to formulate the baryon-quark continuity in
terms of a topology change in the equation of state (EoS) of dense baryonic
matter in analogy to -- and inspired by -- the mapping of the characteristics
of Chern-Simon topological field theory to Kohn-Sham density functional theory
in the fractional quantized Hall effect (FQHE). This is done by translating the
density-dependent characteristics of the skyrmion-half-skyrmion transition
formulated in the presence of hidden local symmetry and (hidden) scale symmetry
to the density-dependent parameters of a renormalization-group approach to
Fermi-liquid fixed point theory. Predictions made in finite nuclei and infinite
compact-star matter are presented.
