Supra soft Omega-open sets and supra soft Omega-regularity

This paper introduces a novel concept of supra-soft topology generated from a specific family of supra-topologies. We define supra-soft $ \omega $-open sets as a new class of soft sets that create a finer topology than the original. We explore the properties of these supra-soft $ \omega $-open sets and assess the validity of related results from ordinary supra-topological spaces within the framework of supra-soft topological spaces. Additionally, we present two new separation axioms: supra-soft $ \omega $-local indiscreteness and supra-soft $ \omega $ -regularity, demonstrating that both are stronger than traditional supra-soft $ \omega $-regularity. We also provide subspace and product theorems for supra-soft $ \omega $-regularity and examine the correspondence between our new supra-soft concepts and their classical counterparts in supra-topology.