Geodesic
Local $\tau$-density of the sum and the superextension of topological spaces
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations, geometry, and topology, Tome 201 (2021), pp. 103-106.

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

In this paper, we study the density and the local density of the superextension of topological spaces. We prove that if $X_{\alpha}$ is a locally $\tau$-dense space for each $\alpha\in A$, then $X=\bigoplus \{X_{\alpha}: \alpha\in A\}$ is also a locally $\tau$-dense space. We also prove that for any infinite $T_{1}$-space, the inequality $ld(\lambda_{c}X)\le ld(X) $ is always valid.
Keywords: topological space, local density, separability, superextension, cardinal number. 
@article{INTO_2021_201_a8,
     author = {F. G. Mukhamadiev},
     title = {Local $\tau$-density of the sum and the superextension of topological spaces},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {103--106},
     publisher = {mathdoc},
     volume = {201},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_201_a8/}
}
TY  - JOUR
AU  - F. G. Mukhamadiev
TI  - Local $\tau$-density of the sum and the superextension of topological spaces
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2021
SP  - 103
EP  - 106
VL  - 201
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2021_201_a8/
LA  - ru
ID  - INTO_2021_201_a8
ER  - 
%0 Journal Article
%A F. G. Mukhamadiev
%T Local $\tau$-density of the sum and the superextension of topological spaces
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2021
%P 103-106
%V 201
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2021_201_a8/
%G ru
%F INTO_2021_201_a8
F. G. Mukhamadiev. Local $\tau$-density of the sum and the superextension of topological spaces. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations, geometry, and topology, Tome 201 (2021), pp. 103-106. http://geodesic.mathdoc.fr/item/INTO_2021_201_a8/

[1] Beshimov R. B., “O slaboi plotnosti topologicheskikh prostranstv”, Dokl. AN RUz., 11 (2000), 10–13 | MR

[2] Makhmud T., Kardinalnoznachnye invarianty prostranstv stseplennykh sistem, Diss. na soisk. uch. step. kand. fiz.-mat. nauk, MGU, M., 1993

[3] Fedorchuk V. V., Filippov V. V., Obschaya topologiya. Osnovnye konstruktsii, Fizmatlit, M., 2006

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

[5] Beshimov R. B., Mukhamadiev F. G., Mamadaliev N. K., “The local density and the local weak density of hyperspaces”, Int. J. Geom., 4:1 (2015), 42–49 | Zbl

[6] Van Mill J., Supercompactness and Wallman Spaces, Amsterdam, 1977 | Zbl