2017
Том 69
№ 6

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

Karchevs’ka L. I.

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.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 10, pp 1567-1576.

Citation Example: Karchevs’ka L. I. On geometric properties of functors of positive-homogenous and semiadditive functionals // Ukr. Mat. Zh. - 2010. - 62, № 10. - pp. 1351–1359.

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