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Keywords:
countably compact space; star-Lindelöf space; absolutely star-Lindelöf space; discretely absolutely star-Lindelöf
Summary:
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.
References:
[1] Bonanzinga, M.: Star-Lindelöf and absolutely star-Lindelöf spaces. Quest. Answers Gen. Topology 16 (1998), 79-104. MR 1642032 | Zbl 0931.54019
[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 0742178
[3] Douwen, E. K. van, Reed, G. M., Roscoe, A. W., Tree, I. J.: Star covering properties. Topology Appl. 39 (1991), 71-103. DOI 10.1016/0166-8641(91)90077-Y | MR 1103993
[4] Engelking, R.: General Topology. Revised and completed edition. Heldermann Verlag Berlin (1989). MR 1039321
[5] Matveev, M. V.: Absolutely countably compact spaces. Topology Appl. 58 (1994), 81-92. DOI 10.1016/0166-8641(94)90074-4 | MR 1280711 | Zbl 0801.54021
[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 1472172 | Zbl 1002.54016
[8] Song, Y.-K.: On some questions on star covering properties. Quest. Answers Gen. Topology 18 (2000), 87-92. MR 1749592 | Zbl 0954.54009
[9] Song, Y.-K.: Discretely star-Lindelöf spaces. Tsukuba J. Math. 25 (2001), 371-382. MR 1869769 | Zbl 1011.54020
[10] Song, Y.-K.: Remarks on star-Lindelöf spaces. Quest. Answers Gen. Topology 20 (2002), 49-51. MR 1910431 | Zbl 1006.54032
[11] Song, Y.-K.: Closed subsets of absolutely star-Lindelöf spaces II. Commentat. Math. Univ. Carol. 44 (2003), 329-334. MR 2026167 | Zbl 1100.54017
[12] Song, Y.-K.: A solution of Matveev's question. Quest. Answers Gen. Topology 20 (2002), 165-168. MR 1931487 | Zbl 1009.54028
[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 0776634 | Zbl 0552.54011
[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 1697629 | Zbl 0974.54011
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