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arXiv · 2102.00296

Selection Games and the Vietoris Space

Christopher Caruvana·Jared Holshouser
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Abstract

We explore the connections between selection games on Hausdorff spaces and their corresponding Vietoris space of compact subsets. These considerations offer a similar relationship as the well-known relationship between $ω$-covers of $X$ and regular open covers of the finite powers of $X$. The primary utility of this method is to establish similar relationships with $k$-covers and the Vietoris space of compact subsets. Particularly, we show that some commonly studied selection principles are equivalent to a related hyperspace being Menger or Rothberger. We then apply these equivalences to correct a flawed argument in a previous paper which attempted to show that a Pawlikowski theorem is true for $k$-covers.

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Christopher Caruvana, Jared Holshouser. 2021-02-26. Selection Games and the Vietoris Space. https://doi.org/10.1016/j.topol.2021.107772

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