遗传不可分解性与中值定理

Periodicity and Indecomposability in Generalized Inverse Limits

In this paper, we consider inverse limits of [0,1] using upper semicontinuous set-valued bonding functions with the intermediate value property. Expanding on classical results by Barge and Martin, we explore the relationship between periodicity in the bonding function and the topology of the corresponding inverse limit. In particular, for an inverse limit of a single upper semicontinuous bonding map with the intermediate value property, we provide sufficient conditions for the existence of a periodic cycle with period not a power of two in the bonding function to imply the existence of an inde…

关于遗传不可分解连续统的注记

Remarks on hereditarily indecomposable continua

我们回顾了遗传不可分解最初由Krasinkiewicz和Minc获得的一个特征，并展示了它如何可能被用来给各种遗传不可分解连续统一的建设。特别是，我们回答了一个问题所提出的Mackowiak和Tymchatyn表明，任何连续的任意重量是一个弱合流图像的遗传不可分解的连续相同的重量。我们提出了两种构造这些原像的方法：（a）通过模型论的方法，利用一阶逻辑的紧性和完备性定理，从度量对应物导出不可数权连续统的这些结果;（b）通过构造从遗传不可分解连续统到Tychonoff立方体的本质映射.我们完成复活的论点，由于凯利超空间的遗传不可分解连续，并显示它如何导致一个点集参数，减少布劳威尔的不动点定理，其三维版本。