Notes on star covering properties

Abstract

In this paper, we show the following statements:
(1) There exists a pseudocompact star Lindelöf Tychonoff space which is not star σ-compact.
(2) There exists a Tychonoff pseudocompact star countable (hence, star Lindelöf) space having a pseudocompact, G_δ regular closed subspace which is not star Lindelöf.
(3) Assuming 2^ℵ₀ = 2^ℵ₁, there exists a normal star countable (hence, star Lindelöf) space having a G_δ regular closed subspace which is not star Lindelöf.
(4) Let X be a space, then A(X) is star Lindelöf if and only if e(X) ≤ ω.
The statement (1) gives a negative answer to Song [13, Remark 2.3].