Related papers: Closed Discrete Selection in the Compact Open Topo…

We introduce the notions of weakly *-concave and weakly naturally quasi-concave correspondence and prove fixed point theorems and continuous selection theorems for these kind of correspondences. As applications in the game theory, by using…

We present a new variation of the classical selection principles $\mathsf{S}_\mathrm{k}(\mathcal A, \mathcal B)$ ($k\in\mathbb N$) and $\mathsf{S}_\mathrm{fin}(\mathcal A, \mathcal B)$ that formally lies between these two properties. As in…

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 study variations on combinatorial games in which, instead of alternating moves, the players bid with discrete bidding chips for the right to determine who moves next. We consider both symmetric and partisan games, and explore differences…

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…

This paper presents discrete convex analysis as a tool for economics and game theory. Discrete convex analysis is a new framework of discrete mathematics and optimization, developed during the last two decades. Recently, it is being…

An open (resp., closed) subset A of a topological space (X, T ) is called C-open (resp., C-closed) set if cl(A) \ A (resp., A \ int(A)) is a countable set. This paper aims to present the concept of C-open and C-closed sets. We first…

We study tightness properties and selective versions of separability in bitopological function spaces endowed with set-open topologies.

We develop a discrete Morse theory for open simplicial complexes $K=X\setminus T$ where $X$ is a simplicial complex and $T$ a subcomplex of $X$. A discrete Morse function $f$ on $K$ gives rise to a discrete Morse function on the order…

We construct algorithms for computation of prices and superhedging strategies for game options in general discrete markets both from the seller and the buyer points of view.

A computation in the continuation monad returns a final result given a continuation, ie. it is a function with type $(X \to R) \to R$. If we instead return the intermediate result at $X$ then our computation is called a selection function.…

In this paper we study a discrete-time semidiscretization and a fully discretization (discrete-time, discrete-state) of an infinite time horizon noncooperative $N$-player differential game. We prove that as either the discretization time…

We prove that the locally convex space $C_{p}(X)$ of continuous real-valued functions on a Tychonoff space $X$ equipped with the topology of pointwise convergence is distinguished if and only if $X$ is a $\Delta$-space in the sense of \cite…

For a completely regular space $X$, denote by $C_p(X)$ the space of continuous real-valued functions on $X$, with the pointwise convergence topology. In this article we strengthen a theorem of O. Okunev concerning preservation of some…

We continue to investigate applications of $k$-covers in function spaces with the compact-open topology.

We study the CHSH inequality from an informational, timing-sensitive viewpoint using game-theoretic probability, which avoids assuming an underlying probability space. The locality loophole and the measurement-dependence…

In this paper, we proved that a clopen version $S_1(C_O, C_O)$ of the Rothberger property and Borel strong measure zeroness are independent. For a zero-dimensional metric space $(X, d)$, $X$ satisfies $S_1(C_O, C_O)$ if, and only if, $X$…

We prove that for each Polish space X, the space C(X) of continuous real-valued functions on X satisfies a strong version of the Pytkeev property, if endowed with the compact-open topology. (This shows that whereas it need not be…

We introduce and study the notion of overt choice for countably-based spaces and for CoPolish spaces. Overt choice is the task of producing a point in a closed set specified by what open sets intersect it. We show that the question of…

The notion of "pseudocompactness" was introduced by Hewitt. The concept of relatively countably compact subspaces were explored by Marjanovic to show that a $\Psi$-space is pseudocompact. A topological space is said to be DRC (DRS) iff it…