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.

arXiv comment12 pages

References in corpus (1)

• Equivariant Movability of Topological Groups

Cited by in corpus (8)

• On Orbits and Bi-invariant Subsets of Binary $G$-Spaces
• Groups of Invertible Binary Operations of a Topological Space
• On Orbit Spaces of Distributive Binary $G$-Spaces
• Bi-Equivariant Fibrations
• On transitive and homogeneous binary $G$-spaces
• On the Transitive Binary $G$-Spaces
• Bi-Equivariant Extensions Of Maps
• Binary transformation groups and topological fields