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Remarks on discretely absolutely star-Lindelöf spaces
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 3, pp. 823-831 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 54B10, 54D20, 54D55
Keywords: countably compact space; star-Lindelöf space; absolutely star-Lindelöf space; discretely absolutely star-Lindelöf 
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Song, Yan-Kui. Remarks on discretely absolutely star-Lindelöf spaces. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 3, pp. 823-831. http://geodesic.mathdoc.fr/item/CMJ_2008_58_3_a16/

[1] Bonanzinga, M.: Star-Lindelöf and absolutely star-Lindelöf spaces. Quest. Answers Gen. Topology 16 (1998), 79-104. | MR | Zbl

[2] Dai, M.: A class of topological spaces which contains all Lindelöf spaces and all separable spaces. Chin. Ann. Math. A4 (1983), 571-575 Chinese. | MR

[3] Douwen, E. K. van, Reed, G. M., Roscoe, A. W., Tree, I. J.: Star covering properties. Topology Appl. 39 (1991), 71-103. | DOI | MR

[4] Engelking, R.: General Topology. Revised and completed edition. Heldermann Verlag Berlin (1989). | MR

[5] Matveev, M. V.: Absolutely countably compact spaces. Topology Appl. 58 (1994), 81-92. | DOI | MR | Zbl

[6] Matveev, M. V.: A Survey on Star-Covering Properties. Topological Atlas preprint No 330 (1998).

[7] Matveev, M. V.: Some questions on property (a). Quest. Answers Gen. Topology 15 (1997), 103-111. | MR | Zbl

[8] Song, Y.-K.: On some questions on star covering properties. Quest. Answers Gen. Topology 18 (2000), 87-92. | MR | Zbl

[9] Song, Y.-K.: Discretely star-Lindelöf spaces. Tsukuba J. Math. 25 (2001), 371-382. | DOI | MR | Zbl

[10] Song, Y.-K.: Remarks on star-Lindelöf spaces. Quest. Answers Gen. Topology 20 (2002), 49-51. | MR | Zbl

[11] Song, Y.-K.: Closed subsets of absolutely star-Lindelöf spaces II. Commentat. Math. Univ. Carol. 44 (2003), 329-334. | MR | Zbl

[12] Song, Y.-K.: A solution of Matveev's question. Quest. Answers Gen. Topology 20 (2002), 165-168. | MR | Zbl

[13] Tall, F. D.: Normality versus collectionwise normality. In: Handbook of Set-Theoretic Topology K. Kunen, J. E. Vaughan North-Holland Amsterdam (1984), pages 685-732. | MR | Zbl

[14] Vaughan, J. E.: Absolute countable compactness and property (a). Talk at 1996 Praha symposium on General Topology.

[15] Yasui, Y., Gao, Z. M.: Spaces in countable web. Houston J. Math. 25 (1999), 327-335. | MR | Zbl