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 ≤ ω1. We investigate the softness of mappings of multiplication of monads generated by these functors.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 10, pp. 1351–1359, October, 2010.
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Karchevs’ka, L.I. On geometric properties of functors of positive-homogenous and semiadditive functionals. Ukr Math J 62, 1567–1576 (2011). https://doi.org/10.1007/s11253-011-0449-4
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DOI: https://doi.org/10.1007/s11253-011-0449-4