Remarks on absolutely star countable spaces

• Autorzy: Yan-Kui Song
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

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

Kategorie tematyczne

• 54D20: Noncompact covering properties (paracompact, Lindel\"of, etc.)
• 54G20: Counterexamples

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 10
• Strony: 1755-1762

Daty

wydano

2013-10-01

online

2013-07-20

Twórcy

autor

Yan-Kui Song

• Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0276-y