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Home » Issues » Archive of Issues » 2023 - 3 issue » pp. 497-522

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Russia Moscow
Year
2023
Volume
33
Issue
3
Pages
497-522
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Section Mathematics
Title Quotient and transversal mappings for topological quasigroups
Author(-s) Ludkowski S.V.a
Affiliations MIREA - Russian Technological Universitya
Abstract This article is devoted to studying the structure of topological left (or right) quasigroups, which play a great role in noncommutative geometry. Quotient and transversal mappings are important in the theory of differentiable manifolds and topological manifolds. Their transversal and quotient mappings are investigated. Necessary and sufficient conditions for their continuity are scrutinized. Examples are given. Homogeneous spaces are investigated related to topological quasigroups and their subquasigroups. For this purpose, the products of special types of topological left (or right) quasigroups, which are called smashed, are investigated. They are used to describe an extensive family of topological nondiscrete left (or right) quasigroups for which transversal mappings are continuous.
Keywords noncommutative geometry, quasigroup, topology, mapping, quotient, transversal, continuity, homogeneous space, product
UDC 515.122.4, 515.16.2, 512.546.8, 512.548.7
MSC 54B05, 54B15, 20N05, 22A22, 22A30
DOI 10.35634/vm230308
Received 4 April 2023
Language Russian
Citation Ludkowski S.V. Quotient and transversal mappings for topological quasigroups, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, vol. 33, issue 3, pp. 497-522.
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