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arXiv · 1812.06379

Closed Discrete Selection in the Compact Open Topology

Christopher Caruvana·Jared Holshouser
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Abstract

In 2017, Tkachuk isolated the closed discrete selection property while working on problems related to function spaces [15]. In this paper we will study the closed discrete selection property and the related games and strategies on $C_k(X)$. Clontz and Holshouser showed previously that the closed discrete selection game on $C_p(X)$ is equivalent to a modification of the point-open game on $X$. In this paper we show that the closed discrete selection game on $C_k(X)$ is equivalent to a modification of the compact-open game on $X$. We also connect discrete selection properties on $C_k(X)$ to a variety of other properties on $X$, $C_k(X)$, and hyperspaces of $X$.

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Christopher Caruvana, Jared Holshouser. 2018-12-16. Closed Discrete Selection in the Compact Open Topology. https://arxiv.org/abs/1812.06379

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