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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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