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

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 a...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2023-06, Vol.272 (6), p.853-865
Main Authors: Babenko, S. P., Badin, A. V.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Topology
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Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06477-z