Topological isomorphism for rank-1 systems
Topological isomorphism for rank-1 systems
复制标题
1 阶系统的拓扑同构
DOI：
10.1007/s11854-016-0001-4
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Aaron Hill
中科院分区：
文献类型：
--
作者：
Su Gao;Aaron Hill
我们定义非简并 1 阶系统的波兰空间 R。每个非简并 1 阶系统都可以被视为无原子、σ 有限测度空间的测度保持变换以及康托空间的同胚。我们完全表征了两个非简并 1 阶系统拓扑同构的情况。我们还分析了 R 上拓扑同构关系的复杂性，表明它是 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${F_\sigma }$$\end{document} 作为 R× R 的子集，可双向约简到 E0。我们还明确描述了非简并 1 阶系统何时与其逆系统在拓扑上同构。
We define the Polish space R of non-degenerate rank-1 systems. Each non-degenerate rank-1 system can be viewed as a measure-preserving transformation of an atomless, σ-finite measure space and as a homeomorphism of a Cantor space. We completely characterize when two non-degenerate rank-1 systems are topologically isomorphic. We also analyze the complexity of the topological isomorphism relation on R, showing that it is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${F_\sigma }$$\end{document} as a subset of R× R and bi-reducible to E0. We also explicitly describe when a non-degenerate rank-1 system is topologically isomorphic to its inverse.