Displaying similar documents to “Two improvements on Tkačenko's addition theorem”

Spaces with large star cardinal number

Yan-Kui Song (2012)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we prove the following statements: (1) For any cardinal κ , there exists a Tychonoff star-Lindelöf space X such that a ( X ) ≥ κ . (2) There is a Tychonoff discretely star-Lindelöf space X such that a a ( X ) does not exist. (3) For any cardinal κ , there exists a Tychonoff pseudocompact σ -starcompact space X such that st - l ( X ) ≥ κ .

Convergence in compacta and linear Lindelöfness

Aleksander V. Arhangel'skii, Raushan Z. Buzyakova (1998)

Commentationes Mathematicae Universitatis Carolinae

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Let X be a compact Hausdorff space with a point x such that X ∖ { x } is linearly Lindelöf. Is then X first countable at x ? What if this is true for every x in X ? We consider these and some related questions, and obtain partial answers; in particular, we prove that the answer to the second question is “yes” when X is, in addition, ω -monolithic. We also prove that if X is compact, Hausdorff, and X ∖ { x } is strongly discretely Lindelöf, for every x in X , then X is first countable. An example of linearly...

On ℒ -starcompact spaces

Yan-Kui Song (2006)

Czechoslovak Mathematical Journal

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A space X is ℒ -starcompact if for every open cover 𝒰 of X , there exists a Lindelöf subset L of X such that S t ( L , 𝒰 ) = X . We clarify the relations between ℒ -starcompact spaces and other related spaces and investigate topological properties of ℒ -starcompact spaces. A question of Hiremath is answered.

On 𝒞 -starcompact spaces

Yan-Kui Song (2008)

Mathematica Bohemica

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A space X is if for every open cover 𝒰 of X , there exists a countably compact subset C of X such that St ( C , 𝒰 ) = X . In this paper we investigate the relations between 𝒞 -starcompact spaces and other related spaces, and also study topological properties of 𝒞 -starcompact spaces.