On selective absolute star-Lindelöfness

A space X is selectively absolutely star-Lindelöf if for any open cover U of X and any sequence (Dn:n∈ω) of dense subsets of X, there are finite sets Fn⊂Dn (n∈ω) such that St(⋃n∈ωFn,U)=X. This notion was introduced by S. Bhowmik [3], and it lies between absolute countable compactness in Matveev [9] and absolute star-Lindelöfness in Bonanzinga [4]. In this paper, we distinguish absolute star-Lindelöfness from selective absolute star-Lindelöfness, and study the general properties of selectively absolutely star-Lindelöf spaces.