相关论文: Preservation of some topological properties under …
Game-theoretic characterizations of selection principles provide a powerful framework for analyzing covering properties through strategic interactions. For a Tychonoff space $X$ and a non-trivial metrizable arc-connected topological group…
In this paper we show that forcings which are strongly proper for stationarily many countable elementary submodels preserve each of the following properties of topological spaces: countably tight; Lindel\"of; Rothberger; Menger; and a…
For a topological space $X$ and a point $x \in X$, consider the following game -- related to the property of $X$ being countably tight at $x$. In each inning $n\in\omega$, the first player chooses a set $A_n$ that clusters at $x$, and then…
The two main results of this work are the following: if a space $X$ is such that player II has a winning strategy in the game $\gone(\Omega_x, \Omega_x)$ for every $x \in X$, then $X$ is productively countably tight. On the other hand, if a…
Iwasa investigated the preservation of various covering properties of opological spaces under Cohen forcing. By improving the argument in Iwasa's paper, we prove that the Rothberger property, the Menger property and selective screenability…
Forcing axioms are generalizations of Baire category principles that allow one to intersect more dense open sets and to do so in a wider variety of circumstances. In this paper we introduce two new forcing axioms related to posets which…
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…
In this article we investigate which compact spaces remain compact under countably closed forcing. We prove that, assuming the Continuum Hypothesis, the natural generalizations to $\omega_1$-sequences of the selection principle and…
We investigate preservation of the Lindel\"of property of topological spaces under forcing extensions. We give sufficient conditions for a forcing notion to preserve several strengthenings of the Lindel\"of property, such as indestructible…
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…
We show that many countable support iterations of proper forcings preserve Souslin trees. We establish sufficient conditions in terms of games and we draw connections to other preservation properties. We present a proof of preservation…
The theta--fan F_theta is the quotient space obtained by identifying the non--isolated points of the product theta \times (omega+1) with a single point \infty. (Here, theta has the discrete topology and omega+1 has the order topology.) We…
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…
An open question of Gruenhage asks if all strategically selectively separable spaces are Markov selectively separable, a game-theoretic statement known to hold for countable spaces. As a corollary of a result by Berner and Juh$\acute{a}$sz,…
In a pursuit-evasion game, a team of pursuers attempt to capture an evader. The players alternate turns, move with equal speed, and have full information about the state of the game. We consider the most restictive capture condition: a…
Consider concurrent, infinite duration, two-player win/lose games played on graphs. If the winning condition satisfies some simple requirement, the existence of Player 1 winning (finite-memory) strategies is equivalent to the existence of…
We extend the weak-strong uniqueness principle for mean-field game (MFG) systems to a broad class of second-order stationary and time-dependent problems. Under standard monotonicity, growth, and coercivity assumptions on the Hamiltonian,…
We show that the following properties are preserved under inverse limits: countable fan-tightness, q+, discrete generation and selective separability. We also present several examples based on inverse limits of countable spaces.
Countable tightness may be destroyed by countably closed forcing. We characterize the indestructibility of countable tightness under countably closed forcing by combinatorial statements similar to the ones Tall used to characterize…
Let S be a topological property of sequences (such as, for example, "to contain a convergent subsequence" or "to have an accumulation point"). We introduce the following open-point game OP(X,S) on a topological space X. In the n'th move,…