  In this paper we investigate the functors of OH of positively homogenous
functionals and OS of semiadditive functionals. We show that OH(X) is AR if and
only if X is openly generated, and OS(X) is AR if and only if X is an openly
generated compactum of weight less than $\omega_1$. Also, we investigate the
multiplication maps of monads generated by the abovementioned functors and
consider when these mappings are soft.
