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On a quasi-component of continuous $$\Omega$$-groups. (Russian) Zbl 0609.22001
Let (G,$$\Omega)$$ be an arbitrary $$\Omega$$-group, $$\Omega_ n$$ is the set of all n-ary operations from $$\Omega$$. If $${\mathcal T}_ 0$$ and $${\mathcal T}_ 1$$ are topologies on G and $$\Omega$$, respectively, such that (G,$${\mathcal T}_ 0)$$ is a topological group for every n and the mapping $$\psi$$ : $$\Omega$$ $${}_ n\times G^ n\to G$$, defined by the rule $$\psi (w,(x_ 1,...,x_ n))=w(x_ 1,...,x_ n)$$ is continuous, then (G,$$\Omega)$$ is called a continuous $$\Omega$$-group. The connections between component and quasicomponent topologies in a continuous $$\Omega$$- group (G,$$\Omega)$$ are investigated in the work.
Reviewer: V.Arnautov
##### MSC:
 22A05 Structure of general topological groups
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