Geodesic
Free topological algebra with separately continuous Mal'tsev operation
Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 4, pp. 89-99

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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, free quasi-Mal'tsev space, quasi-topological group.
Mots-clés : quasi-Mal'tsev space 
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     title = {Free topological algebra with separately continuous {Mal'tsev} operation},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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O. V. Sipacheva; A. A. Solonkov. Free topological algebra with separately continuous Mal'tsev operation. Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 4, pp. 89-99. http://geodesic.mathdoc.fr/item/FAA_2023_57_4_a6/