A Countable Intersection Like Characterization of Star-Lindelöf Spaces

P. Bal

doi:10.15421/242308

A Countable Intersection Like Characterization of Star-Lindelöf Spaces

P. Bal (ICFAI University Tripura)

Abstract

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.

Keywords

star-Lindelöfness; family of closed sets; countable intersection property

MSC 2020

54D20; 54D30; 54D40

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