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.
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Notes
As opposed to \(X^n\) with the usual product topology.
For example, \(\widehat{M}(X)\times \widehat{M}(X)\).
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Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2023, Vol. 57, pp. 89–99 https://doi.org/10.4213/faa4159.
To the blessed memory of Izrael Moiseevich Gel’fand
Translated by O. V. Sipacheva
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Sipacheva, O.V., Solonkov, A.A. Free Topological Algebra with Separately Continuous Mal’tsev Operation. Funct Anal Its Appl 57, 337–345 (2023). https://doi.org/10.1134/S001626632304007X
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DOI: https://doi.org/10.1134/S001626632304007X