On relations between topological and algebraic structures of quasigroups

S. V. Ludkovsky

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 4, pp. 486-498

Résumé

In this paper we study specific features of the relations between topological and algebraic structures of quasigroups and loops. We study the measurability of subsets of topological quasigroups and loops with respect to invariant measures. We study the family of non-measurable subsets in locally compact non-discrete loops. We find out the existence of locally $\mu $-zero subsets that are not $\mu $-zero in a locally compact left quasigroup that is not $\sigma $-compact. We study quotient spaces of measurable spaces on quasigroups. Moreover, we study homogeneous spaces of quasigroups and countable separability of subsets in them.

Détail

Mots-clés : quasigroup, quotient space
Keywords: topology, algebra, homogeneous space, measure, measurable spaces

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