  In this paper we shown that the chain control sets of induced systems on flag
manifolds coincides with their analogous one defined via semigroup actions.
Consequently, any chain control set of the system contains a control set with
nonempty interior and, if the number of the control sets with nonempty interior
coincides with the number of the chain control sets, then the closure of any
control set with nonempty interior is a chain control set.
