Geodesic
Functor of $\mathrm{OS}_{\sigma}$-semiadditive, $\sigma$-smooth functionals
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and topology, Tome 197 (2021), pp. 62-68

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we introduce the functor $\mathrm{OS}_{\sigma}$ of semiadditive $\sigma$-smooth functionals into the category of Tikhonov spaces $\mathrm{Tych}$, which extends the functor $\mathrm{OS}:\mathrm{Comp}\to\mathrm{Comp}$ of semiadditive functionals. We prove that the functor $\mathrm{OS}_{\sigma}:\mathrm{Tych}\to\mathrm{Tych}$ maps $Z$-embeddings into embeddings and the space $\mathrm{OS}_{\sigma}(X)$ is closed in the space of weakly additive $\sigma$-smooth functionals; in particular, $\mathrm{OS}_{\sigma}(X) $ is Hewitt-complete for any Tikhonov space $X\in\mathrm{Tych}$.
Keywords: category, normal functor, semiadditive functional, space of $\sigma$-smooth functionals. 
@article{INTO_2021_197_a6,
     author = {N. K. Mamadaliev},
     title = {Functor of $\mathrm{OS}_{\sigma}$-semiadditive, $\sigma$-smooth functionals},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {62--68},
     publisher = {mathdoc},
     volume = {197},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_197_a6/}
}
TY  - JOUR
AU  - N. K. Mamadaliev
TI  - Functor of $\mathrm{OS}_{\sigma}$-semiadditive, $\sigma$-smooth functionals
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2021
SP  - 62
EP  - 68
VL  - 197
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2021_197_a6/
LA  - ru
ID  - INTO_2021_197_a6
ER  - 
%0 Journal Article
%A N. K. Mamadaliev
%T Functor of $\mathrm{OS}_{\sigma}$-semiadditive, $\sigma$-smooth functionals
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2021
%P 62-68
%V 197
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2021_197_a6/
%G ru
%F INTO_2021_197_a6
N. K. Mamadaliev. Functor of $\mathrm{OS}_{\sigma}$-semiadditive, $\sigma$-smooth functionals. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and topology, Tome 197 (2021), pp. 62-68. http://geodesic.mathdoc.fr/item/INTO_2021_197_a6/