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Funktsional'nyi Analiz i ego Prilozheniya, 2023, Volume 57, Issue 4, Pages 89–99
DOI: https://doi.org/10.4213/faa4159 (Mi faa4159) 		 
Free topological algebra with separately continuous Mal'tsev operation

O. V. Sipacheva, A. A. Solonkov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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DOI: https://doi.org/10.4213/faa4159
Abstract: Topological spaces with separately continuous Mal'tsev operation, called quasi-Mal'tsev spaces, are considered. The existence of the free quasi-Mal'tsev space generated by an arbitrary completely regular Hausdorff space is proved. It is shown that any quasi-Mal'tsev space is a quotient of a free quasi-Mal'tsev space. It is also shown that the topology of a free quasi-Mal'tsev space has a simple and natural description in terms of the generating space. Finally, it is proved that any completely regular Hausdorff quasi-Mal'tsev space is a retract of a quasi-topological group.
Keywords: Mal'tsev operation, quasi-Mal'tsev space, free quasi-Mal'tsev space, quasi-topological group.
Received: 15.09.2023
Revised: 27.09.2023
Accepted: 29.09.2023
English version:
Functional Analysis and Its Applications, 2023, Volume 57, Issue 4, Pages 337–345
DOI: https://doi.org/10.1134/S001626632304007X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: O. V. Sipacheva, A. A. Solonkov, “Free topological algebra with separately continuous Mal'tsev operation”, Funktsional. Anal. i Prilozhen., 57:4 (2023), 89–99; Funct. Anal. Appl., 57:4 (2023), 337–345
Citation in format AMSBIB
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\by O.~V.~Sipacheva, A.~A.~Solonkov
\paper Free topological algebra with separately continuous Mal'tsev operation
\jour Funktsional. Anal. i Prilozhen.
\yr 2023
\vol 57
\issue 4
\pages 89--99
\mathnet{http://mi.mathnet.ru/faa4159}
\crossref{https://doi.org/10.4213/faa4159}
\transl
\jour Funct. Anal. Appl.
\yr 2023
\vol 57
\issue 4
\pages 337--345
\crossref{https://doi.org/10.1134/S001626632304007X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85189081020}
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