Geodesic
Set-theoretic topology and some properties of the closure operation of a collection of sets
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 1, Tome 175 (2020), pp. 105-117.

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

In this paper, we develops an approach to the presentation of set-theoretic topology based on the systematic use of two standard operations: the union operation and the closure operation of a collection of sets (i.e., the closure with respect to the union operation). Definitions of these operations are given and their basic properties are formulated and proved. Based on the results obtained, the foundations of elementary topology are constructed.
Keywords: set, topological space, base of topology, induced topology, product of topological spaces. 
@article{INTO_2020_175_a8,
     author = {S. P. Babenko and A. V. Badin},
     title = {Set-theoretic topology and some properties of the closure operation of a collection of sets},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {105--117},
     publisher = {mathdoc},
     volume = {175},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_175_a8/}
}
TY  - JOUR
AU  - S. P. Babenko
AU  - A. V. Badin
TI  - Set-theoretic topology and some properties of the closure operation of a collection of sets
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2020
SP  - 105
EP  - 117
VL  - 175
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2020_175_a8/
LA  - ru
ID  - INTO_2020_175_a8
ER  - 
%0 Journal Article
%A S. P. Babenko
%A A. V. Badin
%T Set-theoretic topology and some properties of the closure operation of a collection of sets
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2020
%P 105-117
%V 175
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2020_175_a8/
%G ru
%F INTO_2020_175_a8
S. P. Babenko; A. V. Badin. Set-theoretic topology and some properties of the closure operation of a collection of sets. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 1, Tome 175 (2020), pp. 105-117. http://geodesic.mathdoc.fr/item/INTO_2020_175_a8/

[1] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Fizmatlit, M., 2004

[2] Mendelson E., Vvedenie v matematicheskuyu logiku, Nauka, M., 1976

[3] Postnikov M. M., Lektsii po geometrii. Semestr III. Gladkie mnogoobraziya, Nauka, M., 1987

[4] Uorner F., Osnovy teorii gladkikh mnogoobrazii i grupp Li, Mir, M., 1987

[5] Frenkel A., Bar-Khillel I., Osnovaniya teorii mnozhestv, Mir, M., 1966

[6] Shenfild Dzh., Matematicheskaya logika, Nauka, M., 1975