2018•Topology and its ApplicationsOpen access

Remarks on selectively absolute star-Lindelöf spaces

Yan-Kui Song, Wei-Feng Xuan

Abstract

A space X is selectively absolutely star-Lindelöf [1], [3] if for each 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. In this paper, we continue to investigate topological properties of selectively absolute star-Lindelöf spaces, and show the following statements: There exists a Tychonoff selectively a-star-Lindelöf, pseudocompact space X having a regular closed Gδ subset which is not star-Lindelöf (hence not selectively a-star-Lindelöf); Assuming 2ℵ0=2ℵ1, there exists a normal selectively a-star-Lindelöf space X having a regular closed Gδ subset which is not star-Lindelöf (hence not selectively a-star-Lindelöf); An open Fσ-subset of a selectively a-star-Lindelöf space is selectively a-star-Lindelöf; For any cardinal κ, there exists a Tychonoff selectively a-star-Lindelöf, pseudocompact space X such that e(X)≥κ.

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Key concepts: Star (game theory), Tychonoff space, Mathematics, Space (punctuation), Cover (algebra), Combinatorics, Discrete mathematics, Topological space