Displaying similar documents to “Remarks on star covering properties in pseudocompact spaces”

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.

Spaces with large relative extent

Yan-Kui Song (2007)

Czechoslovak Mathematical Journal

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In this paper, we prove the following statements: (1) For every regular uncountable cardinal κ , there exist a Tychonoff space X and Y a subspace of X such that Y is both relatively absolute star-Lindelöf and relative property (a) in X and e ( Y , X ) ≥ κ , but Y is not strongly relative star-Lindelöf in X and X is not star-Lindelöf. (2) There exist a Tychonoff space X and a subspace Y of X such that Y is strongly relative star-Lindelöf in X (hence, relative star-Lindelöf), but Y is not absolutely relative...

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.

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...