  Topology effects have being extensively studied and confirmed in strongly
correlated condensed matter physics. In the large color number limit of QCD,
baryons can be regarded as topological objects -- skyrmions -- and the baryonic
matter can be regarded as a skyrmion matter. We review in this paper the
generalized effective field theory for dense compact-star matter constructed
with the robust inputs obtained from the skyrmion approach to dense nuclear
matter, relying to possible ``emergent" scale and local flavor symmetries at
high density. All nuclear matter properties from the saturation density $n_0$
up to several times $n_0$ can be fairly well described. A uniquely novel -- and
unorthdox -- feature of this theory is the precocious appearance of the
pseudo-conformal sound velocity $v^2_{s}/c^2 \approx 1/3$, with the
non-vanishing trace of the energy momentum tensor of the system. The topology
change encoded in the density scaling of low energy constants is interpreted as
the quark-hadron continuity in the sense of Cheshire Cat Principle (CCP) at
density $\gsim 2n_0$ in accessing massive compact stars. We confront the
approach with the data from GW170817 and GW190425.
