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# Article

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Keywords:
Lindelöf; star-Lindelöf and ${\mathcal L}$-starcompact
Summary:
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.
References:
[1] E. K. van Douwen, G. M. Reed, A. W. Roscoe and I. J. Tree: Star covering properties. Topology Appl. 39 (1991), 71–103. DOI 10.1016/0166-8641(91)90077-Y | MR 1103993
[2] R. Engelking: General Topology, Revised and completed edition. Heldermann Verlag, Berlin, 1989. MR 1039321
[3] G. R. Hiremath: On star with Lindelöf center property. J. Indian Math. Soc. 59 (1993), 227–242. MR 1248966 | Zbl 0887.54021
[4] S. Ikenaga: A class which contains Lindelöf spaces, separable spaces and countably compact spaces. Memories of Numazu College of Technology 18 (1983), 105–108.
[5] R. C. Walker: The Stone-Čech compactification. Berlin, 1974. MR 0380698 | Zbl 0292.54001
[6] M. V. Matveev: A survey on star-covering properties. Topological Atlas, preprint No. 330, 1998.
[7] S. Mrówka: On complete regular spaces. Fund. Math. 41 (1954), 105–106.
[8] Y. Yasui and Z. Gao: Space in countable web. Houston J. Math. 25 (1999), 327–325. MR 1697629

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