Closed subsets of absolutely star-Lindelöf spaces. II. (English) Zbl 1100.54017

Song, Yan-Kui

Commentat. Math. Univ. Carol. 44, No. 2, 329-334 (2003).

Relationships between some generalizations of Lindelöf spaces are studied. It is proved that a regular closed subspace of a “discretely absolutely star Lindelöf” Tychonoff space need not be “CCC-Lindelöf” and that any “linked Lindelöf” (Hausdorff, regular, Tychonoff) space can be represented as a closed \(G_\delta \) “absolutely star Lindelöf” (Hausdorff, regular, Tychonoff) space.
Reviewer’s remarks: (1) The proofs contain several misprints. In the beginning of the proof of Example 2.2 the symbols \(X\) and \(S_1\) are confused, in the definition of \(U_\alpha \) the number \(1\) should be used instead of \(0\), the order of factors in cartesian products is changing from time to time. In the proof of Theorem 2.3 once \(A(S(X))\) should be replaced by \(R(S(X))\).
(2) In the construction of Example 2.2 one can use \(\alpha D\) (one-point compactification) instead of \(\beta D\) (Čech-Stone compactification) which would make the construction more elementary.
[For part I of this paper see Quest. Answers Gen. Topology 22, 131–135 (2004; Zbl 1066.54026).]

Reviewer: Ondřej Kalenda (Praha)

MSC:

54D20	Noncompact covering properties (paracompact, Lindelöf, etc.)
54D35	Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54B05	Subspaces in general topology

Keywords:

discretely absolutely star-Lindelöf space; CCC-Lindelöf space; star-Lindelöf space

Citations:

Zbl 1066.54026