存在混合完全扰乱系统
Mixing completely scrambled system exists
摘要：
我们证明了存在一个拓扑混合同胚是完全混乱的。我们还证明了对任意整数$n\geq 1$，存在拓扑维数连续体$n$支持传递的完全乱序同胚，以及$n$维紧空间支持弱混合的完全乱序同胚.这解决了一个15年前的问题。
英文摘要：
We prove that there exists a topologically mixing homeomorphism which is completely scrambled. We also prove that for any integer $n\geq 1$ there is a continuum of topological dimension $n$ supporting a transitive completely scrambled homeomorphism, and $n$-dimensional compactum supporting a weakly mixing completely scrambled homeomorphism. This solves a 15 year old open problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
