论文标题
连续许多平面嵌入担为手风琴的嵌入
Continuum Many Planar Embeddings of the Knaster Accordion
论文作者
论文摘要
Anusic，Bruin和Cinc询问了哪些遗传可分离的可链连续性（HDCC）具有许多无与伦比的平面嵌入。人们注意到，根据约翰·C·梅耶（John C. Mayer）的嵌入技术（1/x）$ - 曲线，任何是带有ARC射线的压实的HDCC都可能具有此属性。在这里，我们展示了构建$ \ mathfrak {c} $的两种方法 - 经典零零零售额的许多相互不相等的平面嵌入$vλ$ -continuum，$ k $，也称为刀刀手风琴。这两种方法中的第一种产生$ \ mathfrak {c} $ - 许多$ k $的平面嵌入，其图像与$ k $的标准嵌入形象相同，而第二种方法则产生$ \ mathfrak {c} $ - $ k $ $ k $的$ k $的许多嵌入，每个嵌入了$ k $，每个嵌入了该标准的标准。
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.
