On set star-Lindelöf spaces

[EN] A space X is said to be set star-Lindelöf if for each nonempty subset A of X and each collection U of open sets in X such that A ⊆ SU, there is a countable subset V of U such that A ⊆ St(SV, U). The class of set star-Lindelöf spaces lie between the class of Lindel¨of spaces and the class of star-Lindelöf spaces. In this paper, we investigate the relationship between set star-Lindelöf spaces and other related spaces by providing some suitable examples and study the topological properties of set starLindelöf spaces.