AI 中文总结
本文通过超限拓扑博弈为同胚射线空间的序理论树对提供组合特征，还将其应用于多种空间获新拓扑特征，引入射线空间类推广，确定相关子空间性质及特定类射线空间乘积特性。
AI 中文摘要
我们为具有同胚射线空间的序理论树对提供了一种组合特征，回答了Kurkofka和Pitz提出的一个开放问题。该解决方案受超限拓扑博弈引入的启发，这使我们不仅能通过玩家之一的获胜策略存在性来刻画射线空间，还能刻画它们的同胚类。作为这些结果的应用，我们为图论端点空间（从而为Diestel最近解决的一个问题得到另一种解决方案）以及边 - 端点空间和完全超可度量空间获得了新的拓扑特征。我们还引入了射线空间类的一种推广。此外，我们确定对于基数小于连续统的端点空间子空间，散射性质等同于其本身是端点空间的性质。最后，我们确定几类中的射线空间与任何非离散空间的乘积都不是射线空间。
英文摘要
We provide a combinatorial characterization for pairs of order-theoretic trees with homeomorphic ray spaces, answering an open problem proposed by Kurkofka ad Pitz. This solution is inspired by the introduction of a transfinite topological game, which allows us to characterize not only ray spaces through the existence of winning strategies for one of the players, but also their homeomorphic classes. As applications of these results, we obtain a new topological characterization for graph-theoretic end spaces (thus obtaining yet another solution to a recently solved problem of Diestel), as well as for edge-end spaces and completely ultrametrizable spaces. We also introduce a generalization of the class of ray spaces (which is strict, as witnessed by the Sorgenfrey line). Furthermore, we establish that, for subspaces with cardinality less than continuum of end spaces, the scattered property is equivalent to the property of being, itself, an end space. At last, we determine that ray spaces in a couple of classes fail to have their product with any non-discrete space as a ray space.
