Pointless proofs of the Menger and Rothberger games

Equivalence of the Rothberger and $2$-Rothberger Games for Hausdorff Spaces

We prove that in any Hausdorff space, the Rothberger game is equivalent to the $k$-Rothberger game, i.e. the game in which player II chooses $k$ open sets in each move. This result follows from a more general theorem in which we show these games are equivalent to a game we call the restricted Menger game. In this game I knows immediately in advance of playing each open cover how many open sets II will choose from that open cover. This result illuminates the relationship between the Rothberger and Menger games in Hausdorff spaces. The equivalence of these games answers a question posed by Auric…

某些星选择博弈的翻译结果

Translation Results for Some Star-Selection Games

本文研究 Pixley-Roy 超空间和一致空间中的星选择原理，通过将其转化为普通选择原理并应用翻译定理，揭示了星选择博弈与相关博弈及基数不变量之间的联系。

Selective covering properties of product spaces

We study the preservation of selective covering properties, including classic ones introduced by Menger, Hurewicz, Rothberger, Gerlits and Nagy, and others, under products with some major families of concentrated sets of reals. Our methods include the projection method introduced by the authors in an earlier work, as well as several new methods. Some special consequences of our main results are (definitions provided in the paper): \be \item Every product of a concentrated space with a Hurewicz $\sone(\Ga,\Op)$ space satisfies $\sone(\Ga,\Op)$. On the other hand, assuming \CH{}, for each Sierpi…

Topological games and Alster spaces

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_δ subsets. The results include: (1) If Two has a winning strategy in the Menger game on a regular space X, then X is an Alster space. (2) If Two has a winning strategy in the Rothberger game on a topological space X, then the G_δ-topology on X is Lindelof. (3) The Menger game and the compact-open game are (consistently) not dual.

强适当力迫对拓扑性质的保持

Preservation of Topological Properties by Strongly Proper Forcings

本文证明强适当力迫保持拓扑空间的可数紧致度、Lindelöf、Rothberger、Menger 及 Rothberger 策略版本等性质，推广了 Dow、Iwasa 和 Kada 的结果。

关于某些星型选择原理的进一步研究

Further investigations on certain star selection principles

本文进一步研究 Menger、Hurewicz 和 Rothberger 性质的星型版本，利用 Alster 覆盖与临界基数揭示新观察，并借助表格和蕴涵图阐明这些星型选择原理的性质及相互关系。

《Book》中的选择原理与证明

Selection principles and proofs from the Book

本文为拟正规收敛定理、Scheeppers 图最后定理、Menger 博弈定理及 Rothberger 覆盖性质可加性下界四个选择原理基本定理提供简化证明，并由此导出若干新结果。

Selection Games on Hyperspaces

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 hyperspace constructions. This includes results of Lj.D.R. Kočinac, Z. Li, and others. We use selection games to generalize selection principles and we work with strategies of various strengths for these games. The selection games we work with are primarily abstract versions of the selection principles of Rothberger, Menger, and Hurewicz type, as well as game…

群值连续函数空间的性质

Properties of the space of group-valued continuous functions

本文研究群值连续函数空间 $C_p(X,G)$，刻画其可数扇形紧度等拓扑性质，并建立其与 Menger、Rothberger、Hurewicz 等覆盖性质及 $G$-等价、单块性的关系。