Related papers: Selection Games on Hyperspaces
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 $\omega$-covers of…
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-selection principles in Pixley-Roy hyperspaces and uniform spaces.…
We establish relationships between various topological selection games involving the space of minimal usco maps with various topologies, including the topology of pointwise convergence and the topology of uniform convergence on compact…
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 topologies on the space of continuous real-valued functions.…
In this paper we define some combinatorial principles to characterize spaces $X$ whose hyperspace satisfies some variation of some classical star selection principle. Specifically, the variations characterized are the selective and absolute…
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 occur across different topologies, including the topology of…
Following the decision-theoretic approach to game theory, we extend the analysis of Epstein & Wang and of Di Tillio from hierarchies of preference relations to hierarchies of choice functions. We then construct the universal choice…
We present a unified approach, based on dominating families in binary relations, for the study of topological properties defined in terms of selection principles and the games associated to them.
For a Hausdorff space $X$ we denote be $2^X$ the family of all closed subsets of $X$. In this paper we continue to research relationships between closure -type properties of hyperspaces over a space $X$ and covering properties of $X$. We…
We review some selected recent results concerning selection principles in topology and their relations with several topological constructions.
Often, a given selection game studied in the literature has a known dual game. In dual games, a winning strategy for a player in either game may be used to create a winning strategy for the opponent in the dual. For example, the Rothberger…
In these notes we introduce and investigate two new games called R-nw-selective game and the M-nw-selective game. These games naturally arise from the corresponding selection principles involving networks introduced in \cite{BG}.
We investigate game-theoretic properties of selection principles related to weaker forms of the Menger and Rothberger properties. For appropriate spaces some of these selection principles are characterized in terms of a corresponding game.…
In this paper, we prove a theorem about embedding of some partially ordered topological spaces in topological hyperspaces equipped with Fell topology. Then we give some examples to show that the map defining the embedding may not be…
We add to the theory of preservation of topological properties under forcing. In particular, we answer a question of Gilton and Holshouser in a strong sense, showing that if player II has a winning strategy in the strong countable fan…
For nearly three decades, spatial games have produced a wealth of insights to the study of behavior and its relation to population structure. However, as different rules and factors are added or altered, the dynamics of spatial models often…
Let E be a locally compact second countable Hausdorff space and F the pertaining family of all closed sets. We endow F respectively with the Fell-topology, the upper Fell topology or the upper Vietoris-topology and investigate weak…
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 incorporate a class of subsemigroups of the semigroup of…
Finite games in normal form and their mixed extensions are a corner stone of noncooperative game theory. Often generic finite games and their mixed extensions are considered. But the properties which one expects in generic games and the…
For a Tychonoff space $X$, we denote by $(C(X), \tau_k, \tau_p)$ the bitopological space of all real-valued continuous functions on $X$ where $\tau_k$ is the compact-open topology and $\tau_p$ is the topology of pointwise convergence. In…