On Transitive and Homogeneous Binary $$\boldsymbol{G}$$-Spaces

In this paper, the notions of transitivity and homogeneity in binary $$G$$ -spaces are studied. These notions coincide for distributive binary $$G$$ -spaces. For compact $$G$$ , it is shown that distributive transitive binary $$G$$ -spaces are coset spaces with a suitably defined binary $$G$$ -action. Homogeneous binary $$G$$ -spaces are topologically homogeneous and are separated into distinct stabilization types. Examples of each type are constructed.