On geometric properties of functors of positive-homogenous and semiadditive functionals

Abstract

We investigate the functor $OH$ of positive-homogenous functionals and the functor $OS$ of semiadditive functionals. We prove that $OH(X)$ is an absolute retract if and only if $X$ is an open-generated compactum, and $OS(X)$ is an absolute retract if and only if $X$ is an opengenerated compactum of weight $≤ ω_1$. We investigate the softness of mappings of multiplication of monads generated by these functors.