论文标题
具有应用的超规模空间的粗糙结构
Coarse structure of ultrametric spaces with applications
论文作者
论文摘要
我们展示了如何将所有可分离的超级空间分解成整个简短版本的“乐高”组合。为此，我们介绍了大型度量空间的度量分辨率，这些分辨率描述了如何将空间分解成大致独立的零件。我们使用这些度量分辨率来定义大型度量空间的粗略分离结合，这提供了一种以“粗糙独立的方式”将大型度量空间连接到对方的方法。我们使用这些概念分别在可分离和适当的度量空间的类别中构建通用空间，分别为渐近维$ 0 $。为此，我们概括了Dranishnikov和Zarichnyi以及Nagórko和Bell的类似结果。但是，新应用程序是渐近维度$ 0 $的适当度量空间的通用空间，这使这些作者避免了。我们将描述一些可以用作这种通用空间的可数组的描述。
We show how to decompose all separable ultrametric spaces into a "Lego" combinations of scaled versions of full simplices. To do this we introduce metric resolutions of large scale metric spaces, which describe how a space can be broken up into roughly independent pieces. We use these metric resolutions to define the coarse disjoint union of large scale metric spaces, which provides a way of attaching large scale metric spaces to each other in a "coarsely independent way". We use these notions to construct universal spaces in the categories of separable and proper metric spaces of asymptotic dimension $0$, respectively. In doing so we generalize a similar result of Dranishnikov and Zarichnyi as well as Nagórko and Bell. However, the new application is a universal space for proper metric spaces of asymptotic dimension $0$, something that eluded those authors. We finish with a description of some countable groups that can serve as such universal spaces.
