8 citations · 26 across the 13 of their papers we have counts for
13 papers · 1 filter
On Large Covers and the Strong Closed Discrete Game
Christopher Caruvana, Jared Holshouser
We strengthen a recent selection game equivalence proved by L. Chiozini involving spaces and their associated spaces of continuous real-valued functions. This strengthening establi…
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…
An Excursion with Divergence Properties
Christopher Caruvana
In this note, we compare and contrast various selective divergence properties such as the properties of being discretely selective and selectively highly divergent. We identify and…
On Traditional Menger and Rothberger Variations
Christopher Caruvana, Steven Clontz, Jared Holshouser
We present a comprehensive report on the relationships between variations of the Menger and Rothberger selection properties with respect to -covers and -covers in the most ge…
Translation Results for some Selection Games with Minimal Cusco Maps
Christopher Caruvana, Jared Holshouser
We establish relationships between various topological selection games involving the space of minimal cusco maps into the real line and the underlying domain. These connections occ…
The Hurewicz Property and the Vietoris Hyperspace
Christopher Caruvana
In this note, we characterize when the Vietoris space of compact subsets of a given space has the Hurewicz property in terms of a selection principle on the given space itself usin…
Translation Results for Some Star-Selection Games
Christopher Caruvana, Jared Holshouser
We continue to explore the ways in which high-level topological connections arise from connections between fundamental features of the spaces, in this case focusing on star-selecti…
Selection Games with Minimal Usco Maps
Christopher Caruvana
We establish relationships between various topological selection games involving the space of minimal usco maps with various topologies, including the topology of pointwise converg…
On strategies for selection games related to countable dimension
Christopher Caruvana, Steven Clontz
Two selection games from the literature, and , are known to characterize countable dimension among certain spaces. Thi…
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…