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Lindelöf; star-Lindelöf and ${\mathcal L}$-starcompact
A space $X$ is $\mathcal L$-starcompact if for every open cover $\mathcal U$ of $X,$ there exists a Lindelöf subset $L$ of $X$ such that $\mathop {\mathrm St}(L,{\mathcal U})=X.$ We clarify the relations between ${\mathcal L}$-starcompact spaces and other related spaces and investigate topological properties of ${\mathcal L}$-starcompact spaces. A question of Hiremath is answered.
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