Displaying similar documents to “New properties of the concentric circle space and its applications to cardinal inequalities”

A semifilter approach to selection principles

Lubomyr Zdomsky (2005)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we develop the semifilter approach to the classical Menger and Hurewicz properties and show that the small cardinal 𝔤 is a lower bound of the additivity number of the σ -ideal generated by Menger subspaces of the Baire space, and under 𝔲 < 𝔤 every subset X of the real line with the property Split ( Λ , Λ ) is Hurewicz, and thus it is consistent with ZFC that the property Split ( Λ , Λ ) is preserved by unions of less than 𝔟 subsets of the real line.

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 ) .