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Abstract <p>Distributive subsets of the group of all invertible continuous binary operations on a topological space are considered, and it is proved that the subgroups generated by them are also distributive. A criterion for the distributivity of a binary action of a topological group <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(G\)</EquationSource> <!--BMatMGU2570055Gevorkyan-m3--> </InlineEquation> on a space <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(X\)</EquationSource> <!--BMatMGU2570055Gevorkyan-m4--> </InlineEquation> is obtained. The concept of transitive binary <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(G\)</EquationSource> <!--BMatMGU2570055Gevorkyan-m5--> </InlineEquation>-space is introduced, and a classification of transitive distributive binary <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(G\)</EquationSource> <!--BMatMGU2570055Gevorkyan-m6--> </InlineEquation>-spaces is given in the case of a compact group <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(G\)</EquationSource> <!--BMatMGU2570055Gevorkyan-m7--> </InlineEquation>.</p>

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On the Transitive Binary \(\boldsymbol{G}\)-Spaces

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • P. S. Gevorgyan

摘要

Abstract

Distributive subsets of the group of all invertible continuous binary operations on a topological space are considered, and it is proved that the subgroups generated by them are also distributive. A criterion for the distributivity of a binary action of a topological group \(G\) on a space \(X\) is obtained. The concept of transitive binary \(G\) -space is introduced, and a classification of transitive distributive binary \(G\) -spaces is given in the case of a compact group \(G\) .