Displaying similar documents to “A semifilter approach to selection principles”

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.

Splitting ω -covers

Winfried Just, Andreas Tanner (1997)

Commentationes Mathematicae Universitatis Carolinae

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The authors give a ZFC example for a space with Split ( Ω , Ω ) but not Split ( Λ , Λ ) .

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 ) .