On geometric properties of the functors of positively homogenous and semiadditive functionals

Abstract

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.