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Remarks on Star-Hurewicz Spaces

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Song Y.-K.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2013
|
tom 61
|
nr 3
247-255
EN
A space X is star-Hurewicz if for each sequence (𝒰ₙ: n ∈ ℕ) of open covers of X there exists a sequence (𝓥ₙ: n ∈ ℕ) such that for each n, 𝓥ₙ is a finite subset of 𝒰ₙ, and for each x ∈ X, x ∈ St(⋃ 𝓥ₙ,𝒰ₙ) for all but finitely many n. We investigate the relationship between star-Hurewicz spaces and related spaces, and also study topological properties of star-Hurewicz spaces.
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Absolutely strongly star-Hurewicz spaces

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Song Y.-K.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
A space X is absolutely strongly star-Hurewicz if for each sequence (Un :n ∈ℕ/ of open covers of X and each dense subset D of X, there exists a sequence (Fn :n ∈ℕ/ of finite subsets of D such that for each x ∈X, x ∈St(Fn; Un) for all but finitely many n. In this paper, we investigate the relationships between absolutely strongly star-Hurewicz spaces and related spaces, and also study topological properties of absolutely strongly star-Hurewicz spaces.
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Remarks on absolutely star countable spaces

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Song Y.-K.
Open Mathematics
|
2013
|
tom 11
|
nr 10
1755-1762
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).
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