On Θ-J^α-Open and Ω-J^β-Open Sets in Structured Ideal Topological Spaces

Abstract

This paper introduces two novel classes of open sets in the realm of ideal topological

spaces, termed Θ-J^α-open and Ω-J^β-open sets. We investigate the topological

behavior, closure characteristics, and functional implications of these sets in generalized

continuity frameworks. The relationship between these sets is rigorously analyzed and

used to derive several forms of continuity decompositions. Our contributions broaden

the understanding of how these new set types fit into ideal topologies and highlight their impact on the overall structure of such spaces.