2019
Том 71
№ 7

# Karchevs’ka L. I.

Articles: 2
Brief Communications (Ukrainian)

### ON the Openness of Functors of k-Nonexpanding and Weakly Additive Functionals

Ukr. Mat. Zh. - 2013. - 65, № 11. - pp. 1567–1574

We study the property of openness of the functors for k -nonexpanding and weakly additive functionals. In particular, it is shown that these functors preserve the openness of mappings between finite compact sets but they are not open.

Article (Ukrainian)

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

Ukr. Mat. Zh. - 2010. - 62, № 10. - pp. 1351–1359

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.