Groups of Binary Operations and Binary $G$-Spaces

Abstract

The group of continuous binary operations on a topological space is studied; its relationship with the group of homeomorphisms is established. The category of binary $G$-spaces and bi-equivariant maps is constructed, which is a natural extension of the category of $G$-spaces and equivariant maps. Results related to the foundations of the theory of binary $G$-spaces are obtained.