On the Transitive Binary $$\boldsymbol{G}$$-Spaces

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 $$G$$ .