A Countable Intersection Like Characterization of Star-Lindelöf Spaces

There have been various studies on star-Lindelöfness but they always explain it in terms of open coverings. So, we have demonstrated in this study a connection between star-Lindelöfness and the family of closed sets that resembles countable intersection property of Lindelöf space. We show that a topological space $X$ is star-Lindelöf if and only if every closed subset's family of $X$ not having the modified non-countable intersection property have non-empty intersection.