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Set-Theoretic Topology and Some Properties of the Closure Operation of a Collection of Sets

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Abstract

In this paper, we develop 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, we present the foundations of elementary topology.

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Authors and Affiliations

  1. Bauman Moscow State Technical University, Moscow, Russia

    S. P. Babenko

  2. M. V. Lomonosov Moscow State University, Moscow, Russia

    A. V. Badin

Authors
  1. S. P. Babenko
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  2. A. V. Badin
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Correspondence to S. P. Babenko.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 175, Proceedings of the XVII All-Russian Youth School-Conference “Lobachevsky Readings-2018,” November 23-28, 2018, Kazan. Part 1, 2020.

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Babenko, S.P., Badin, A.V. Set-Theoretic Topology and Some Properties of the Closure Operation of a Collection of Sets. J Math Sci 272, 853–865 (2023). https://doi.org/10.1007/s10958-023-06477-z

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  • DOI: https://doi.org/10.1007/s10958-023-06477-z

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