齐次平面连续统的完全分类
A complete classification of homogeneous plane continua
摘要：
证明了非退化齐次平面连续统同胚于单位圆、伪弧或伪弧的圆。因此，任何平面齐次紧都有$X \times Z$的形式，其中$X$是一个点或这三个齐次平面连续统之一，而$Z$是一个有限集或康托尔集。本文的主要技术结果是伪弧的一个新的特征：一个非退化连续统是伪弧同胚的当且仅当它是遗传不可分解的，并且跨度为零。
英文摘要：
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.
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。
