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arXiv · 1405.7208

Combinatorial aspects of selective star covering properties in $Ψ$-spaces

Boaz Tsaban
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Abstract

Which Isbell--Mrówka spaces ($Ψ$-spaces) satisfy the star version of Menger's and Hurewicz's covering properties? Following Bonanzinga and Matveev, this question is considered here from a combinatorial point of view. An example of a $Ψ$-space that is (strongly) star-Menger but not star-Hurewicz is obtained. The PCF-theory function $κ\mapsto\cof([κ]^\alephes)$ is a key tool. Using the method of forcing, a complete answer to a question of Bonanzinga and Matveev is provided. The results also apply to the mentioned covering properties in the realm of Pixley--Roy spaces, to the extent of spaces with these properties, and to the character of free abelian topological groups over hemicompact $k$ spaces.

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Boaz Tsaban. 2015-07-09. Combinatorial aspects of selective star covering properties in $Ψ$-spaces. https://doi.org/10.1016/j.topol.2015.05.082

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