Displaying similar documents to “Splitting ω -covers”

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.

Some properties of relatively strong pseudocompactness

Guo-Fang Zhang (2008)

Czechoslovak Mathematical Journal

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In this paper, we study some properties of relatively strong pseudocompactness and mainly show that if a Tychonoff space X and a subspace Y satisfy that Y ⊂ Int Y ¯ and Y is strongly pseudocompact and metacompact in X , then Y is compact in X . We also give an example to demonstrate that the condition Y ⊂ Int Y ¯ can not be omitted.

A semifilter approach to selection principles II: τ * -covers

Lubomyr Zdomsky (2006)

Commentationes Mathematicae Universitatis Carolinae

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Developing the idea of assigning to a large cover of a topological space a corresponding semifilter, we show that every Menger topological space has the property ⋃ fin ( 𝒪 , T * ) provided ( 𝔲 < 𝔤 ) , and every space with the property ⋃ fin ( 𝒪 , T * ) is Hurewicz provided ( Depth + ( [ ω ] ℵ 0 ) ≤ 𝔟 ) . Combining this with the results proven in cited literature, we settle all questions whether (it is consistent that) the properties P and Q [do not] coincide, where P and Q run over ⋃ fin ( 𝒪 , Γ ) , ⋃ fin ( 𝒪 , T ) , ⋃ fin ( 𝒪 , T * ) , ⋃ fin ( 𝒪 , Ω ) , and ⋃ fin ( 𝒪 , 𝒪 ) .

New properties of the concentric circle space and its applications to cardinal inequalities

Shu Hao Sun, Koo Guan Choo (1991)

Commentationes Mathematicae Universitatis Carolinae

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It is well-known that the concentric circle space has no G δ -diagonal nor any countable point-separating open cover. In this paper, we reveal two new properties of the concentric circle space, which are the weak versions of G δ -diagonal and countable point-separating open cover. Then we introduce two new cardinal functions and sharpen some known cardinal inequalities.