A note on discretely absolutely star-Lindelöf spaces

Abstract

In this paper, we prove the following statements:(1)~If $X$ is a normal discretely absolutely star-Lindel{ö}fspace with $e(X)<{\omega }_1$, then the Alexandroff duplicate $A(X)$of $X$ is discretely absolutely star-Lindel{ö}f.(2)~If $X$ is a space with $e(X)\ge {\omega }_1$, then $A(X)$ isnot discretely absolutely star-Lindel{ö}f.The two statements answer a question raised by Song.