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Let P be a topological property. A space X is said to be star P if whenever 
is an open cover of X, there exists a subspace A ⊆ X with property P such that 
, where 
. In this paper, we investigate the relationships among star Lindelöf spaces, star almost Lindelöf spaces and star weakly Lindelöf spaces, and also study topological properties of star weakly Lindelöf spaces.
Mathematics Subject Classification (2020):
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