Specific types of Lindelöfness and compactness based on novel supra soft operator

The aim of this study was to originate six types of generalized compactness and Lindelöfness in the frame of supra soft topological spaces (or SSTSs) based on the approaches of supra soft somewhere dense sets (or SS-sd-sets) and the SS-sd-closure operator, named SS-sd-almost compact (Lindelöf) spaces, SS-sd-approximately compact (Lindelöf) spaces and SS-sd-mildly compact (Lindelöf) spaces. The essential properties of each type of the aforementioned notions were studied. Specifically, we studied the invariance of these notions under specific types of soft mappings. Moreover, the relationships among these notions and between corresponding notions were discussed. Furthermore, the equivalence among them was proved under the SS-sd-partition condition. Finally, we provided a diagram to summarize these relationships with the support of concrete counterexamples.