Homotopy classes of maps between Knaster continua

Continuum Many Planar Embeddings of the Knaster Accordion

Anusic, Bruin, and Cinc have asked which hereditarily decomposable chainable continua (HDCC) have uncountably many mutually inequivalent planar embeddings. It was noted, as per the embedding technique of John C. Mayer with the $\sin(1/x)$-curve, that any HDCC which is the compactification of a ray with an arc likely has this property. Here, we show two methods for constructing $\mathfrak{c}$-many mutually inequivalent planar embeddings of the classic Knaster $V Λ$-continuum, $K$, also referred to as the Knaster accordion. The first of these two methods produces $\mathfrak{c}$-many planar embed…

链状连续统上的线性序

Linear orders on chainable continua

研究链状连续统上依赖于链序列和超滤子的线性序，证明弧上有2种、Warsaw正弦曲线有4种、Knaster连续统有2^c种不同超滤子序，并刻画Suslinean性质与序同构于[0,1]的关系。

弧状连续统平面嵌入中可数集的可接近性

Accessibility of countable sets in plane embeddings of arc-like continua

本文研究弧状连续统的平面嵌入问题，证明了在特定条件下逆向极限存在使给定可数集所有点均可接近的嵌入，并应用于 Knaster 连续统及构造了作为平面同胚吸引子的新嵌入。

弧状连续体、整个函数的Julia集和Eremenko猜想

Arc-like continua, Julia sets of entire functions, and Eremenko's Conjecture

本文研究了分离型整个函数的Julia集拓扑性质，证明了其Julia连续体为弧状连续体，并构造了具有特定性质的函数，与Eremenko猜想相关。