  We argue that the entanglement Chern number proposed recently is invariant
under the adiabatic deformation of a gapped many-body groundstate into a {\it
disentangled/purified} one, which implies a partition of the Chern number into
subsystems (disentangled Chern number). We generalize the idea to another
topological number, the Z$_2$ Berry phase for a system with particle-hole
symmetry, and apply it to a groundstate in a weak topological phase where the
Chern number vanishes but the groundstate nevertheless has edge states. This
entanglement Berry phase is especially useful for characterizing random systems
with nontrivial edge states.
