Refinement of Bratteli-Vershik models
Refinement of Bratteli-Vershik models
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发表时间：
2020-10
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通讯作者：
T. Shimomura
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作者：
T. Shimomura
在零维系统中，Bratteli-Vershik模型可以建立在某些闭集上，这些闭集在本文中称为“准截面”。零维系统和拟截面的三元组的拓扑共轭类与Bratteli-Vershik模型的拓扑共轭类之间存在双射对应。因此，如果我们得到某些精化的准截面，我们就可以得到精化的Bratteli-Vershik模型。基本集是这样的细化准部分，带来了相应的Bratteli-Vershik模型的“封闭性”。给出了基本集存在性的一个直接证明。对拟截面和基本集进行了深入的研究。此外，Bratteli-Vershik模型考虑最小集合会很方便。在这一点上，我们证明了存在的Bratteli-Vershik模型，其最小集是适当的顺序。另一方面，我们可以得到关于Bratteli-Vershikizability条件或决定性的某些改进。
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.