Displaying similar documents to “Spaces with large relative extent”

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.

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.

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.