相关论文: Telgarsky's conjecture may fail

The article studies topological games that arise in the study of the continuity of operations in groups with topology, such as paratopological and semitopological groups. These games are modifications of the Banach--Mazur game. Given a…

The classical result of Landau on the existence of kings in finite tournaments (=finite directed complete graphs) is extended to continuous tournaments for which the set X of players is a compact Hausdorff space. The following partial…

In this paper, the Pazy's Fixed Point Theorems of monotone $\alpha-$nonexpansive mapping $T$ are proved in a uniformly convex Banach space $E$ with the partial order "$\leq$". That is, we obtain that the fixed point set of $T$ with respect…

In this paper, we construct two hypergraphs which exhibit the following properties. We first construct a hypergraph $G_{CP}$ and show that Breaker wins the Maker-Breaker game on $G_{CP}$, but Chooser wins the Chooser-Picker game on…

Let $X$ be a partially ordered set with the property that each family of order intervals of the form $[a,b],[a,\rightarrow )$ with the finite intersection property has a nonempty intersection. We show that every directed subset of $X$ has a…

~This paper presents a general result that allows for establishing a link between the Kolmogorov-Marcinkiewicz-Zygmund strong law of large numbers and Feller's strong law of large numbers in a Banach space setting. Let $\{X, X_{n}; n \geq…

Consider the following two-player game on the edges of $K_n$, the complete graph with $n$ vertices: Starting with an empty graph $G$ on the vertex set of $K_n$, in each round the first player chooses $b \in \mathbb{N}$ edges from $K_n$…

We consider turn-based stochastic two-player games with a combination of a parity condition that must hold surely, that is in all possible outcomes, and of a parity condition that must hold almost-surely, that is with probability 1. The…

We work in set-theory without choice ZF. Denoting by AC(N) the countable axiom of choice, we show in ZF+AC(N) that the closed unit ball of a uniformly convex Banach space is compact in the convex topology (an alternative to the weak…

What parts of classical descriptive set theory done in Polish spaces still hold for more general topological spaces, possibly T0 or T1, but not T2 (i.e. not Hausdorff)? This question has been addressed by Victor Selivanov in a series of…

The classical Banach-Mazur game characterizes sets of first category in a topological space. In this work, we show that an effectivized version of the game yields a characterization of sets of effective first category. Using this, we give a…

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…

We show that a pair of Kolmogorov-Loveland betting strategies cannot win on every non-Martin-L\"of random sequence if either of the two following conditions is true: (I) There is an unbounded computable function $g$ such that both betting…

A well-known result of R. Pol states that a Banach space $X$ has property ($\mathcal{C}$) of Corson if and only if every point in the weak*-closure of any convex set $C \subseteq B_{X^*}$ is actually in the weak*-closure of a countable…

In this paper, we prove the following Theorems 1. An extremally disconnected space $X$ has the semi-Menger property if and only if One does not have a winning strategy in the game $G_{fin}(sO,sO)$. 2. An extremally disconnected space $X$…

Determining a Nash equilibrium in a $2$-player non-zero sum game is known to be PPAD-hard (Chen and Deng (2006), Chen, Deng and Teng (2009)). The problem, even when restricted to win-lose bimatrix games, remains PPAD-hard (Abbott, Kane and…

We formulate the $(n,k)$ Coset Monogamy Game, in which two players must extract complementary information of unequal size ($k$ bits vs. $n-k$ bits) from a random coset state without communicating. The complementary information takes the…

A Banach space is said to have the ball-covering property (abbreviated BCP) if its unit sphere can be covered by countably many closed, or equivalently, open balls off the origin. Let $K$ be a locally compact Hausdorff space and $X$ be a…

In this note we show that every Banach space $X$ not containing $\ell_1^n$ uniformly and with unconditional basis contains an arbitrarily distortable subspace.

Player ONE chooses a meager set and player TWO, a nowhere dense set per inning. They play $\omega$ many innings. ONE's consecutive choices must form a (weakly) increasing sequence. TWO wins if the union of the chosen nowhere dense sets…