Borel and Hausdorff hierarchies in topological spaces of Choquet games and their effectivization
Borel and Hausdorff hierarchies in topological spaces of Choquet games and their effectivization
复制标题
Choquet博弈拓扑空间中的Borel和Hausdorff层次及其实现
DOI：
10.1017/s096012951300025x
复制
发表时间：
2013
影响因子：
0.5
通讯作者：
Serge Grigorieff
中科院分区：
文献类型：
--
作者：
Verónica Becher;Serge Grigorieff
在波兰空间中完成的经典描述集合论的哪些部分仍然适用于更一般的拓扑空间，可能是T 0或T 1，但不适用于T 2（即不适用于豪斯多夫）？这个问题已解决Selivanov在一系列文件集中在代数域。最近，de布雷希特考虑了拟波兰空间，一个包含可数基连续域和波兰空间的框架。在本文中，我们提出了替代统一拓扑空间，我们称之为近似空间。在Choquet博弈中，Nonempty玩家在这些空间上有固定策略。近似空间的一个自然真子类与拟波兰空间类重合。我们研究了近似空间中的Borel和Hausdorff差族，重温了其他拓扑空间所做的工作。我们还考虑这些结果的有效性的问题。
What parts of the classical descriptive set theory done in Polish spaces still hold for more general topological spaces, possibly T 0 or T 1, but not T 2 (i.e. not Hausdorff)? This question has been addressed by Selivanov in a series of papers centred on algebraic domains. And recently it has been considered by de Brecht for quasi-Polish spaces, a framework that contains both countably based continuous domains and Polish spaces. In this paper, we present alternative unifying topological spaces, that we call approximation spaces. They are exactly the spaces for which player Nonempty has a stationary strategy in the Choquet game. A natural proper subclass of approximation spaces coincides with the class of quasi-Polish spaces. We study the Borel and Hausdorff difference hierarchies in approximation spaces, revisiting the work done for the other topological spaces. We also consider the problem of effectivization of these results.