论文标题
Bratteli-Vershik模型的完善
Refinement of Bratteli-Vershik models
论文作者
论文摘要
在零维系统中，Bratteli-Vershik模型可以建立在本文中称为“准区域”的某些封闭集上。在零维系统和准区域的拓扑结合类别与Bratteli-vershik模型的拓扑结合类别之间存在着徒的对应关系。因此，如果我们获得某些精制的准段，我们可以获得精致的Bratteli-Vershik模型。基本集合是如此精致的准部分，在相应的Bratteli-vershik模型上带来了“关闭属性”。我们直接证明了基本集的存在。对准段和基本集进行了详尽的调查。此外，Bratteli-Vershik型号涉及最少的集合将很方便。为此，我们展示了将最小设置正确订购的Bratteli-Vershik模型的存在。另一方面，我们可以在Bratteli-Vershikizizizizizizizizizizizizizizizizizizizizizizizizizizioncions或果断性方面获得一定的改进。
In the zero-dimensional systems, the Bratteli-Vershik models can be built upon certain closed sets that are called `quasi-sections' in this article. There exists a bijective correspondence between the topological conjugacy classes of triples of zero-dimensional systems and quasi-sections and the topological conjugacy classes of Bratteli-Vershik models. Therefore, we can get refined Bratteli-Vershik models if we get certain refined quasi-sections. The basic sets are such refined quasi-sections that bring `closing property' on the corresponding Bratteli-Vershik models. We show a direct proof on the existence of basic sets. Thorough investigations on quasi-sections and basic sets are done. Furthermore, it would be convenient for the Bratteli-Vershik models to concern minimal sets. To this point, we show the existence of the Bratteli-Vershik models whose minimal sets are properly ordered. On the other hand, we can get certain refinements with respect to the Bratteli-Vershikizability condition or the decisiveness.
