On $C$-properties of the space of idempotent robability measures

In the work it is shown that the space of idempotent probability measures with compact supports is kappa-metrizable if the given Tychonoff space is kappa-metrizable. It is constructed a series of max-plus-convex subfunctors of the functor of idempotent probability measures with compact supports. Further, it is established that the functor of idempotent probability measures with the compact supports preserves openness of continuous maps.