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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 11, Issue 10


Volume 13 (2015)

Remarks on absolutely star countable spaces

Yan-Kui Song
Published Online: 2013-07-20 | DOI: https://doi.org/10.2478/s11533-013-0276-y


We prove the following statements: (1) every Tychonoff linked-Lindelöf (centered-Lindelöf, star countable) space can be represented as a closed subspace in a Tychonoff pseudocompact absolutely star countable space; (2) every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented as a closed G δ-subspace in a Hausdorff (regular, Tychonoff) absolutely star countable space; (3) there exists a pseudocompact absolutely star countable Tychonoff space having a regular closed subspace which is not star countable (hence not absolutely star countable); (4) assuming $$2^{\aleph _0 } = 2^{\aleph _1 }$$, there exists an absolutely star countable normal space having a regular closed subspace which is not star countable (hence not absolutely star countable).

MSC: 54D20; 54G20

Keywords: Pseudocompactness; Star countable; Absolutely star countable; Centered Lindelöf; Linked-Lindelöf

  • [1] Aiken L.P., Star-covering properties: generalized ψ-spaces, countability conditions, reflection, Topology Appl., 2011, 158(13), 1732–1737 http://dx.doi.org/10.1016/j.topol.2011.06.032Web of ScienceCrossrefGoogle Scholar

  • [2] Alas O.T., Junqueira L.R., van Mill J., Tkachuk V.V., Wilson R.G., On the extent of star countable spaces, Cent. Eur. J. Math., 2011, 9(3), 603–615 http://dx.doi.org/10.2478/s11533-011-0018-yCrossrefGoogle Scholar

  • [3] Alas O.T., Junqueira L.R., Wilson R.G., Countability and star covering properties, Topology Appl., 2011, 158(4), 620–626 http://dx.doi.org/10.1016/j.topol.2010.12.012CrossrefWeb of ScienceGoogle Scholar

  • [4] Bonanzinga M., Star-Lindelöf and absolutely star-Lindelöf spaces, Questions Answers Gen. Topology, 1998, 16(2), 79–104 Google Scholar

  • [5] Bonanzinga M., Matveev M.V., Centered-Lindelöfness versus star-Lindelöfness, Comment. Math. Univ. Carolin., 2000, 41(1), 111–122 Google Scholar

  • [6] Bonanzinga M., Matveev M.V., Closed subspaces of star-Lindelöf and related spaces, East-West J. Math., 2000, 2(2), 171–179 Google Scholar

  • [7] van Douwen E.K., Reed G.M., Roscoe A.W., Tree I.J., Star covering properties, Topology Appl., 1991, 39(1), 71–103 http://dx.doi.org/10.1016/0166-8641(91)90077-YCrossrefWeb of ScienceGoogle Scholar

  • [8] Engelking R., General Topology, Sigma Ser. Pure Math., 6, Heldermann, Berlin, 1989 Google Scholar

  • [9] Matveev M.V., Absolutely countably compact spaces, Topology Appl., 1994, 58, 81–92 http://dx.doi.org/10.1016/0166-8641(94)90074-4CrossrefGoogle Scholar

  • [10] Matveev M.V., How weak is weak extent?, Topology Appl., 2002, 119(2), 229–232 http://dx.doi.org/10.1016/S0166-8641(01)00061-XCrossrefGoogle Scholar

  • [11] Matveev M.V., A survey on star-covering properties, preprint available at Topology Atlas (http://at.yorku.ca/topology), #330 Google Scholar

  • [12] van Mill J., Tkachuk V.V., Wilson R.G., Classes defined by stars and neighbourhood assignments, Topology Appl., 2007, 154(10), 2127–2134 http://dx.doi.org/10.1016/j.topol.2006.03.029CrossrefWeb of ScienceGoogle Scholar

  • [13] Mrówka S., On completely regular spaces, Fund. Math., 1954, 41, 105–106 Google Scholar

  • [14] Song Y., Remarks on countability and star covering properties, Topology Appl., 2011, 158(9), 1121–1123 http://dx.doi.org/10.1016/j.topol.2011.03.006Web of ScienceCrossrefGoogle Scholar

  • [15] Song Y.-K., Shi W.-X., Subspaces of absolutely star-Lindelöf spaces, Houston J. Math., 2004, 30(2), 451–457 Google Scholar

  • [16] Tall F.D., Normality versus collectionwise normality, In: Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, 685–732 Google Scholar

  • [17] Vaughan J.E., On the product of a compact space with an absolutely countably compact space, In: Papers on General Topology and Applications, Amsterdam, August 15–18, 1994, Ann. New York Acad. Sci., 788, 1996, 203–208 Google Scholar

  • [18] Vaughan J.E., Absolute countable compactness and property (a), 8th Topological Symposium, Prague, August 18–24, 1996 (talk) Google Scholar

About the article

Published Online: 2013-07-20

Published in Print: 2013-10-01

Citation Information: Open Mathematics, Volume 11, Issue 10, Pages 1755–1762, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-013-0276-y.

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© 2013 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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