  The interacting bosons in one-dimensional inversion-symmetric superlattices
are investigated from the topological aspect. The complete phase diagram is
obtained by an atomic-limit analysis and quantum Monte Carlo simulations and
comprises three kinds of phases: superfluid, persisted charge-density-wave and
Mott insulators, and emergent insulators in the presence of nearest-neighbor
hoppings. We find that all emergent insulators are topological, which are
characterized by the Berry phase $\pi$ and a pair of degenerate in-gap boundary
states. The mechanism of the topological bosonic insulators is qualitatively
discussed and the ones with higher fillings can be understood as a
$\frac{1}{3}$-filling topological phase on a background of trivial
charge-density-wave or Mott insulators.
