Knaster手风琴的连续多平面嵌入
Continuum Many Planar Embeddings of the Knaster Accordion
摘要：
Anusic、Bruin和Cinc提出了一个问题：哪些遗传可分解的可链连续统（HDCC）具有不可数的互不等价的平面嵌入。据指出，按照嵌入技术的约翰C。Mayer用$\sin(1/x)$-曲线证明了任何HDCC都可能具有这种性质，HDCC是一条带有弧的射线的紧化。在这里，我们展示了两种方法来构建$\mathfrak{c}$-许多相互不等价的平面嵌入的经典Knaster $V Λ$-连续体，$K$，也被称为Knaster手风琴。这两种方法中的第一种产生$\mathfrak{c}$-$K$的许多平面嵌入，其所有图像具有与$K$的标准嵌入的图像不同的可访问点的集合，而第二种方法产生$\mathfrak{c}$-$K$的许多嵌入，每个嵌入都保留标准嵌入中的所有点的可访问性。
英文摘要：
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 embeddings of $K$, all of whose images have a different set of accessible points from the image of the standard embedding of $K$, while the second method produces $\mathfrak{c}$-many embeddings of $K$, each of which preserve the accessibility of all points in the standard embedding.
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