On Pairwise Almost Quasi-Continuous Mappings in Bitopological Spaces

Almost quasi-continuity, introduced by Popa (1978) in the setting of classical topological spaces, has played an important role in the development of generalized continuity concepts. Motivated by the increasing interest in continuity notions within bitopological frameworks, this paper extends the concept of almost quasi-continuity to bitopological spaces through the introduction of pairwise almost quasicontinuous mappings. Several equivalent characterizations of this new class are established, and its fundamental properties are investigated. Furthermore, the relationships between pairwise almost quasicontinuity and other generalized pairwise continuity concepts are examined. As a main result, it is shown that pairwise almost quasi-continuity is equivalent to pairwise semi-weak continuity. These results enrich the theory of generalized continuity in bitopological spaces and provide a solid foundation for future studies of mappings between spaces equipped with two interacting topologies.