Soft structural Oxtoby–Rose operators and their generated topologies

In this study, we introduce the notion of soft Oxtoby–Rose operators within the framework of abstract measurable soft spaces, extend the classical concept of lower-density operators, and explore their essential characteristics. Subsequently, we delve into the so-called soft Oxtoby–Rose topologies (soft OR-topologies), the soft topologies generated by soft Oxtoby–Rose operators. We examine the key features and definitions associated with soft OR-topologies. Specifically, we demonstrate that within soft OR-topologies, Baire category soft sets, soft locally closed sets, and Borel soft sets are all equivalent. We wrap up this research by analyzing various soft topological properties linked to soft OR-topologies.