论文标题
用给定的Higson或二元电晕构建粗大空间
Constructing a coarse space with a given Higson or binary corona
论文作者
论文摘要
对于任何紧凑的Hausdorff space $ k $，我们构建了一个规范的粗略结构$ \ MATHCAL E_ {x，k} $在$ k $的隔离点的集合$ x $上。该结构有两个属性： $ \ bullet $如果一个限制的粗大空间$（x，\ mathcal e）$是可元的，则其粗糙结构$ \ mathcal e $与Higson Compactification $ \ bar x $ x $ x $ $ x $; $ \ bullet $紧凑的hausdorff space $ k $与粗空间的higson紧凑型（x，x，\ mathcal e_ {x，k}）$相吻合，如果$ x $ in $ k $中的space $ k $是frechet-urchet-yrysohn。 这意味着，如果以下条件之一成立，则紧凑的Hausdorff Space $ k $对某些限制性粗糙空间的Higson Corona是同质的：（i）$ k $完全正常； （ii）$ k $具有权重$ w（k）\leΩ_1$和字符$χ（k）<\ mathfrak p $。在CH下，每一个（零维）紧凑的Hausdorff重量$ \leΩ_1$对某些细胞粉状粗糙空间的Higson（分别二进制）电晕是同型。
For any compact Hausdorff space $K$ we construct a canonical finitary coarse structure $\mathcal E_{X,K}$ on the set $X$ of isolated points of $K$. This construction has two properties: $\bullet$ If a finitary coarse space $(X,\mathcal E)$ is metrizable, then its coarse structure $\mathcal E$ coincides with the coarse structure $\mathcal E_{X,\bar X}$ generated by the Higson compactification $\bar X$ of $X$; $\bullet$ A compact Hausdorff space $K$ coincides with the Higson compactification of the coarse space $(X,\mathcal E_{X,K})$ if the set $X$ is dense in $K$ and the space $K$ is Frechet-Urysohn. This implies that a compact Hausdorff space $K$ is homeomorphic to the Higson corona of some finitary coarse space if one of the following conditions holds: (i) $K$ is perfectly normal; (ii) $K$ has weight $w(K)\leω_1$ and character $χ(K)<\mathfrak p$. Under CH every (zero-dimensional) compact Hausdorff space of weight $\leω_1$ is homeomorphic to the Higson (resp. binary) corona of some cellular finitary coarse space.
