Remarks on selectively absolute star-Lindelöf spaces.

A space X is selectively absolutely star-Lindelöf [1,3] if for each open cover U of X and any sequence ( D n : n ∈ ω ) of dense subsets of X , there are finite sets F n ⊆ D n ( n ∈ ω ) such that S t ( ⋃ n ∈ ω F n , U ) = X . In this paper, we continue to investigate topological properties of selectively absolute star-Lindelöf spaces, and show the following statements: (1) There exists a Tychonoff selectively a-star-Lindelöf, pseudocompact space X having a regular closed G δ subset which is not star-Lindelöf (hence not selectively a-star-Lindelöf); (2) Assuming 2 ℵ 0 = 2 ℵ 1 , there exists a normal selectively a-star-Lindelöf space X having a regular closed G δ subset which is not star-Lindelöf (hence not selectively a-star-Lindelöf); (3) An open F σ -subset of a selectively a-star-Lindelöf space is selectively a-star-Lindelöf; (4) For any cardinal κ , there exists a Tychonoff selectively a-star-Lindelöf, pseudocompact space X such that e ( X ) ≥ κ . [ABSTRACT FROM AUTHOR]