Cantor 扇上的传递映射
Transitive mappings on the Cantor fan
AI总结：
本文在拓扑结构相对简单的 Cantor 扇上构造了传递同胚，通过商空间和 Mahavier 乘积等四种不同技术实现，并展示了该方法可构造出逆极限为 Lelek 扇的传递函数。
摘要：
文献中可以找到许多允许传递同胚的连续统。圆可能是允许此类同胚的最简单的非退化连续统。另一方面，此类连续统的大多数已知示例具有复杂的拓扑结构。例如，它们是不可分解的（如伪弧或 Knaster 桶柄连续统），或者它们不是不可分解的但具有其他复杂的拓扑结构，例如分支点的稠密集（如 Sierpiński 地毯）或端点的稠密集（如 Lelek 扇）。在本文中，我们继续寻找具有允许传递同胚的更简单拓扑结构的连续统。我们在 Cantor 扇上构造了一个传递同胚。在我们的方法中，我们使用了四种不同的技术，每种技术都给出了 Cantor 扇上传递同胚的独特构造：两种使用紧度量空间与 Cantor 集乘积的商空间的技术，以及两种使用紧度量空间上闭关系的 Mahavier 乘积的技术。我们还展示了我们使用闭关系的 Mahavier 乘积的技术如何用于在 Cantor 扇 X 上构造传递函数 f，使得逆极限 projlim(X,f) 是一个 Lelek 扇。
英文摘要：
Many continua that admit a transitive homeomorphism may be found in the literature. The circle is probably the simplest non-degenerate continuum that admits such a homeomorphism. On the other hand, most of the known examples of such continua have a complicated topological structure. For example, they are {indecomposable} (such as the pseudo-arc or the Knaster bucket-handle continuum), or they are {not indecomposable} but have some other complicated topological structure, such as a dense set of ramification points (such as the Sierpi\' nski carpet) or a dense set of end-points (such as the Lelek fan). In this paper, we continue our mission of finding continua with simpler topological structures that admit a transitive homeomorphism.} We construct a transitive homeomorphism on the Cantor fan. {In our approach, we use four different techniques, each of them giving a unique construction of a transitive homeomorphism on the Cantor fan:} two techniques using quotient spaces of products of compact metric spaces and Cantor sets, and two using Mahavier products of closed relations on compact metric spaces. {We also demonstrate how our technique using Mahavier products of closed relations may be used to } construct a transitive function $f$ on a Cantor fan $X$ such that $\varprojlim(X,f)$ is a Lelek fan.
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。
