2019
Том 71
№ 7

All Issues

Karchevs’ka L. I.

Articles: 2
Brief Communications (Ukrainian)

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

Karchevs’ka L. I.

↓ Abstract   |   Full text (.pdf)

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

Karchevs’ka L. I.

↓ Abstract   |   Full text (.pdf)

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.