论文标题
大型空间的选择游戏
Selection Games on Hyperspaces
论文作者
论文摘要
在本文中，我们将拓扑空间上的选择原理与其超空间之一的相应选择原理联系起来。我们将技术统一并从已知的关于常见超空间构建的选择原理的结果中概括。这包括LJ.D.R.的结果Kočinac，Z。Li等。我们使用选择游戏来概括选择原则，并使用这些游戏的各种优势策略。我们与之合作的选择游戏主要是Rothberger，Menger和Hurewicz类型的选择原理的抽象版本，以及可数粉丝的紧密度和选择性可分离性的游戏。我们与之合作的超空间结构是越野和秋季拓扑，无论是上层还是完整的，都是由封闭场景的理想产生的。使用新技术，我们能够将拓扑结构之间的直接连接扩展到与这些构造相关的选择游戏之间的连接。无论游戏的长度，要执行的选择类型或所考虑的策略的强度，这种扩展过程都可以。
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 games of countable fan tightness and selective separability. The hyperspace constructions that we work with are the Vietoris and Fell topologies, both upper and full, generated by ideals of closed sets. Using a new technique we are able to extend straightforward connections between topological constructs to connections between selection games related to those constructs. This extension process works regardless of the length of the game, the kind of selection being performed, or the strength of the strategy being considered.
