On $\alpha $-embedded sets and extension of mappings

Olena Karlova

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.

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Displaying similar documents to “On $α$ -embedded sets and extension of mappings”