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/

[1] Arkhangelskii A. V., Topologicheskie prostranstva funktsii, MGU, M., 1989

[2] Ivanov A. V., Kardinalnoznachnye invarianty i funktory v kategorii bikompaktov, Diss. na soisk. uch. step. doktora fiz.-mat. nauk, Petrozavodsk, 1985

[3] Makhmud T., “O kardinalnykh invariantakh prostranstv stseplennykh sistem”, Vestn. MGU. Ser. 1. Mat. Mekh., 1995, no. 4, 14–19

[4] Mukhamadiev F. G., “Nekotorye kardinalnye svoistva $N_{\tau}^{\varphi}$-yadra prostranstva $X$”, Itogi nauki tekhn. Sovr. mat. prilozh. Temat. obz., 144, 2018, 117–121

[5] Fedorchuk V. V., Filippov V. V., Obschaya topologiya. Osnovnye konstruktsii, MGU, M., 2006

[6] Engelking R., Obschaya topologiya, Mir, M., 1986

[7] Beshimov R. B., Mukhamadiev F. G., “Some cardinal properties of complete linked systems with compact elements and absolute regular spaces”, Math. Aeterna., 3:8 (2013), 625–633 | Zbl

[8] Juhasz I., Cardinal Functions in Topology. Ten Years Later, Math. Centrum, Amsterdam, 1980 | Zbl