Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2020, Volume 175, Pages 105–117
DOI: https://doi.org/10.36535/0233-6723-2020-175-105-117 (Mi into580) 		 
Set-theoretic topology and some properties of the closure operation of a collection of sets

S. P. Babenkoa, A. V. Badinb

a Bauman Moscow State Technical University
b Lomonosov Moscow State University
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DOI: https://doi.org/10.36535/0233-6723-2020-175-105-117
Abstract: 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.
Document Type: Article
UDC: 515.12
MSC: 54A05
Language: Russian
Citation: S. P. Babenko, A. V. Badin, “Set-theoretic topology and some properties of the closure operation of a collection of sets”, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 175, VINITI, Moscow, 2020, 105–117
Citation in format AMSBIB
\Bibitem{BabBad20}
\by S.~P.~Babenko, A.~V.~Badin
\paper Set-theoretic topology and some properties of the closure operation of a collection of sets
\inbook Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018»,
November 23-28, 2018, Kazan. Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 175
\pages 105--117
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into580}
\crossref{https://doi.org/10.36535/0233-6723-2020-175-105-117}
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