On geometric properties of functors of positive-homogenous and semiadditive functionals - Karchevs’ka, L. I. (Ukrains’kyi Matematychnyi Zhurnal, 2010)
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.