论文标题
有限树上的等效映射
Equicontinuous mappings on finite trees
论文作者
论文摘要
如果$ x $是有限的树，而$ f \ colon x \ longrightArrow x $是一张地图，则作为本文的主要定理，我们找到了八个条件，每个条件都等于$ f $是等效的。仅命名获得的一些结果：$ f $的等效性等同于以下事实：对于某些$ n \ in \ atmathbb {n} $，满足$ a \ subsetneq f^n [a] $满足的弧$ a \ subseteq x $。这也等同于这样一个事实，即对于某些非原始超级滤波器$ u $，功能$ f^u \ colon x \ longrightArrow x $是连续的（换句话说，$ f $的等效性失败等效于Ellis剩余$ g \ in E（x，f）的Ellis剩余$ g \ g f的每个$ element $ element $ element $ element $ elemention的失败。证明中使用的工具之一是Ramsey理论结果，称为Hindman定理。我们的结果概括了Vidal-Escobar和García-Ferreira所显示的结果，并补充了Bruckner和Ceder，Mai和Camargo，Rincón和Uzcátegui的结果。
If $X$ is a finite tree and $f \colon X \longrightarrow X$ is a map, as the Main Theorem of this paper we find eight conditions, each of which is equivalent to the fact that $f$ is equicontinuous. To name just a few of the results obtained: the equicontinuity of $f$ is equivalent to the fact that there is no arc $A \subseteq X$ satisfying $A \subsetneq f^n[A]$ for some $n\in \mathbb{N}$. It is also equivalent to the fact that for some nonprincial ultrafilter $u$, the function $f^u \colon X \longrightarrow X$ is continuous (in other words, failure of equicontinuity of $f$ is equivalent to the failure of continuity of $every$ element of the Ellis remainder $g\in E(X,f)^*$). One of the tools used in the proofs is the Ramsey-theoretic result known as Hindman's theorem. Our results generalize the ones shown by Vidal-Escobar and García-Ferreira, and complement those of Bruckner and Ceder, Mai, and Camargo, Rincón and Uzcátegui.
