Selective Version of Star-Semi-Lindelöfness in (a) Topological Spaces

In this paper, we deal with the properties (a)R-star-semi-Lindelöf and (a)M-star-semi-Lindelöf in (a)topological spaces. These properties are interesting as every (a)R^s-separable space is (a)R-star-semi-Lindelöf and every (a)^s-semi-Lindelöf space is (a)R-star-semi-Lindelöf but not every (a)R-star-semi-Lindelöf space is (a)R^s-separable or (a)^s-semi-Lindelöf. It is shown that if an (a)topological space X is the union of countably many (a)-open and (a)Rstar-semi-Lindelöf subspaces, then X is (a)R-star-semi-Lindelöf. Similar results are obtained in the context of (a)M-star-semi-Lindelöf spaces. Further, suitable and required counterexamples are given.