On Some Selective Strengthenings of Certain Star Covering Properties.

‎‎‎We present some properties recently introduced by Bal and Bhowmik: the H-, R-, and M-star Lindelöfness. These properties are defined via selection principles involving the star operator and lie between covering properties (in particular, star-covering properties) and certain selective strengthenings of separability. This dual perspective leads to several implications and connections with known properties, some of which we present. Additionally, we provide several examples. In particular, we prove the existence of a Tychonoff M-star Lindelöf space of cardinality that is not R-star Lindelöf, thereby answering a question posed by Bal and Bhowmik.