Related papers: Translation Results for some Selection Games with …
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 connect selection principles on a topological space to corresponding selection principles on one of its hyperspaces. We unify techniques and generalize theorems from the known results about selection principles for common…
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 $C_k(X)$.…
In this paper, we defined two new games - the mildly Menger game and the compact-clopen game. In a zero-dimensional space, the Menger game is equivalent to the mildly Menger game and the compact-open game is equivalent to the compact-clopen…
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.…
The relationship between topology and dynamics of complex systems has motivated continuing interest from the scientific community. In the present work, we address this interesting topic from the perspective of simple games, involving two…
We initiate the study of simple games from the point of view of combinatorial topology. The starting premise is that the losing coalitions of a simple game can be identified with a simplicial complex. Various topological constructions and…
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…
In this paper we study connections between topological games such as Rothberger, Menger and compact-open, and relate these games to properties involving covers by G_{\delta} subsets. The results include: (1) If Two has a winning strategy in…
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…
Two selection games from the literature, $G_c(\mathcal O,\mathcal O)$ and $G_1(\mathcal O_{zd},\mathcal O)$, are known to characterize countable dimension among certain spaces. This paper studies their perfect- and limited-information…
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 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. In particular we show that player II can win the discrete…
We present a general way of defining various reduction games on \omega\ which "represent" corresponding topologically defined classes of functions. In particular, we will show how to construct games for piecewise defined functions, for…
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…
Covering spaces of graphs have long been useful for studying expanders (as "graph lifts") and unique games (as the "label-extended graph"). In this paper we advocate for the thesis that there is a much deeper relationship between…
This paper is a twofold contribution. First, it contributes to the problem of enumerating some classes of simple games and in particular provides the number of weighted games with minimum and the number of weighted games for the dual class…
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.…
We study the smallest intersecting and enclosing ball problems in Euclidean spaces for input objects that are compact and convex. They link and unify many problems in computational geometry and machine learning. We show that both problems…