On the descriptive complexity of homogeneous continua

Simply connected均匀连续体不被弧分开

Simply connected homogeneous continua are not separated by arcs

我们表明，局部连通，单连通齐次连续不分离的弧。我们问几个问题的启发类似的问题，在几何群论的齐次连续。

Homogeneous continua that are not separated by arcs

We prove that if $X$ is a strongly locally homogeneous and locally compact separable metric space and $G$ is a region in $X$ with $\dim G=2$, then $G$ is not separated by any arc in $G$.

连续齐次的遗传不可分解连续统是树状的

Continuously homogeneous hereditarily indecomposable continua are tree-like

证明连续齐次且遗传不可分解的连续统是树状的，推广了Bing、Rogers和Sturm的相关结果，部分回答了Lewis关于这类连续统是否齐次的问题。

A complete classification of homogeneous plane continua

We show that every non-degenerate homogeneous plane continuum is homeomorphic to either the unit circle, the pseudo-arc, or the circle of pseudo-arcs. It follows that any planar homogenous compactum has the form $X \times Z$, where $X$ is a either a point or one of these three homogeneous plane continua, and $Z$ is a finite set or the Cantor set. The main technical result in this paper is a new characterization of the pseudo-arc: a non-degenerate continuum is homeomorphic to the pseudo-arc if and only if it is hereditarily indecomposable and has span zero.

多单调开齐次locally connected平面连续统

More monotone open homogeneous locally connected plane continua

本文构造了Sierpienski曲线的一个连续分解，将其分解为其中一个为圆弧的无循环连续域。这个分解然后被用来构造Sierpienski曲线的另一个连续分解。由此产生的分解空间是同胚的连续得到的Sierpienski曲线，并确定其互补域之一的边界上的两个点。这一结果表明，暗示有许多拓扑不同的一维局部连通的平面连续统是关于单调开映射齐次。

Generalized Cantor manifolds and indecomposable continua

We review results concerning homogeneous compacta and discuss some open questions. It is established that indecomposable continua are Alexandroff (resp., Mazurkiewicz, or strong Cantor) manifolds with respect to the class of all continua. We also provide some new proofs of Bing's theorems about separating metric compacta by hereditarily indecomposable compacta.