6 papers · 1 filter
An Adaptation of the Vietoris Topology for Ordered Compact Sets
Christopher Caruvana, Jared Holshouser
We discuss a natural topology on powers of a space that is inspired by the Vietoris topology on compact subsets. We then place this topology in context with other product topologie…
Selection Games and the Vietoris Space
Christopher Caruvana, Jared Holshouser
We explore the connections between selection games on Hausdorff spaces and their corresponding Vietoris space of compact subsets. These considerations offer a similar relationship…
Selection Games on Hyperspaces
Christopher Caruvana, Jared Holshouser
In this paper we connect selection principles on a topological space to corresponding selection principles on one of its hyperspaces. We unify techniques and generalize theorems fr…
Selection Games on Continuous Functions
Christopher Caruvana, Jared Holshouser
In this paper we study the selection principle of closed discrete selection, first researched by Tkachuk in [13] and strengthened by Clontz, Holshouser in [3], in set-open topologi…
Closed Discrete Selection in the Compact Open Topology
Christopher Caruvana, Jared Holshouser
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 selectio…
Limited Information Strategies and Discrete Selectivity
Steven Clontz, Jared Holshouser
We relate the property of discrete selectivity and its corresponding game, both recently introduced by V.V. Tkachuck, to a variety of selection principles and point picking games.…