Tri-Expandability and Product Spaces in Tri-Topological Spaces

In this paper, we introduce and investigate the notion of tri-expandability in tri-topological spaces as a natural generalization of expandability in classical topological spaces. We establish fundamental characterizations of tri-expandable spaces and explore their behavior under product operations. The main results include a comprehensive study of the relationships between various forms of tri-expandability and their connections to classical expandability properties. We prove that tri-expandability is preserved under certain product constructions and provide necessary and sufficient conditions for a tri-topological space to be tri-expandable. Our findings extend the classical theory of expandable spaces to the multi-topological setting and reveal new structural properties that are unique to the tri-topological framework. Several illustrative examples demonstrate the richness of the theory and highlight the differences from the classical case.