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Bibliographic Details
Main Authors:	Gevorgyan, Pavel S., Melendez, Quitzeh Morales
Format:	Preprint
Published:	2025
Subjects:	General Topology
Online Access:	https://arxiv.org/abs/2509.05847
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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.