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
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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/