Displaying similar documents to “On 𝒞 -starcompact spaces”

Remarks on star covering properties in pseudocompact spaces

Yan-Kui Song (2013)

Mathematica Bohemica

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Let P be a topological property. A space X is said to be star P if whenever 𝒰 is an open cover of X , there exists a subspace A ⊆ X with property P such that X = St ( A , 𝒰 ) , where St ( A , 𝒰 ) = ⋃ { U ∈ 𝒰 : U ∩ A ≠ ∅ } . In this paper, we study the relationships of star P properties for P ∈ { Lindel ö f , compact , countablycompact } in pseudocompact spaces by giving some examples.

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...

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...