Novel Classes of Soft Disconnectedness: Soft Properly and Super Properly Semi-Disconnected Spaces

Within the realm of uncertainty modeling using soft set theory, topological structures provide a flexible framework for analysis. In this paper, we introduce and study two refined classes of disconnectedness: soft properly semi-disconnected (soft PS-disconnected) and soft super properly semi-disconnected (soft SPS-disconnected) spaces. Using soft semi-open and soft α-open sets, we provide several characterizations of these new spaces, relying particularly on the behavior of soft regular open sets and soft semiclosures to establish necessary and sufficient conditions. We then establish a strict topological hierarchy, proving that soft SPS-disconnectedness implies soft PS-disconnectedness. Both conditions are shown to be strictly stronger than soft S-disconnectedness, yet we demonstrate that neither guarantees standard soft disconnectedness. Beyond this internal hierarchy, we link these soft properties to classical topological spaces via generated and soft product topologies. Finally, we establish the preservation of these soft spaces under soft surjective irresolute functions. Throughout the text, we construct specific counterexamples to confirm that the logical implications within our hierarchy are strictly irreversible.