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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

Issues

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

Abstract

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

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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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