## 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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### References:

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