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Remarks on discretely absolutely star-Lindelöf spaces. (English) Zbl 1174.54015

Summary: We prove the following statements:
(1) There exists a Hausdorff Lindelöf space  \(X\) such that the Alexandroff duplicate  \(A(X)\) of  \(X\) is not discretely absolutely star-Lindelöf.
(2) If \(X\)  is a regular Lindelöf space, then \(A(X)\)  is discretely absolutely star-Lindelöf.
(3) If \(X\)  is a normal discretely star-Lindelöf space with \(e(X)< \omega _1\), then \(A(X)\) is discretely absolutely star-Lindelöf.

MSC:

54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54B10 Product spaces in general topology
54D55 Sequential spaces
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