Abstract
In this paper, we prove the following statements (1) There exists a Hausdorff Lindelof space X such that the Alexandroff duplicate A(X) of X is not discretely absolutely star-Lindelof. (2) If X is a regular Lindelof space, then A(X) is discretely absolutely star-Lindelof. (3) If X is a normal discretely star-Lindelof space with e(X) < ω 1, then A(X) is discretely absolutely star-Lindelof.
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