ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 54H11, 22A30 Movsisyan, Movses, Yerevan State University, Armenia Topological quasigroups with identities A quasigroup (loop) Q(A) is called topological, if Q is a topological space and the operations A, A^{−1}, ^{−1}A are continuous in Q, where A^{−1} and ^{−1}A are the right and left inverses for A, respectively. Theorem. A groupoid Q(·) is a topological distributive quasigroup iff there exists a topological commutative Moufang loop Q(+) such that the operation (·) is defined as follows:

x · y = φ(x) + ψ(y),

where φ, ψ are topological automorphisms of Q(+) and automorphisms of Q(·), φ(x) + ψ(x) = x, x + φ(x) ∈ K_{Q} (is the kernel of Q(+)) for all x ∈ Q. A characterization of the topological quasigroups with other identities will be presented.