On the Decomposability of Selje Topological Spaces

The development of generalized closed set theory has significantly expanded the structural foundations of modern topology. In this paper, we investigate decomposition properties within Selje Topological Spaces, a relationally structured extension of classical topology. By introducing and analyzing SJ-locally closed and SJ-R#α-locally closed sets, we establish a systematic decomposition framework that extends classical locally closed set representations into the Selje setting. Structural characterizations are obtained using Selje closure and interior operators, and inclusion relationships among Selje closed, R#α-closed, and locally closed classes are rigorously examined. The study further introduces SJ-R#α-LC continuous mappings and investigates their functional behavior under inverse images and composition. These results provide a refined hierarchical structure within Selje topology and strengthen its decomposition theory. The proposed framework enhances the theoretical depth of Selje Topological Spaces and offers a foundation for further research in relational topology, generalized continuity, and interdisciplinary applications such as network analysis and data-driven topological modeling.