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Keywords:
countably compact space; star-Lindelöf space; absolutely star-Lindelöf space; discretely absolutely star-Lindelöf
Summary:
In this paper, we prove the following statements: \item {(1)} There exists a Hausdorff Lindelöf space $X$ such that the Alexandroff duplicate $A(X)$ of $X$ is not discretely absolutely star-Lindelöf. \item {(2)} If $X$ is a regular Lindelöf space, then $A(X)$ is discretely absolutely star-Lindelöf. \item {(3)} If $X$ is a normal discretely star-Lindelöf space with $e(X)< \omega _1$, then $A(X)$ is discretely absolutely star-Lindelöf.
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