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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