论文标题
通过粗糙的接近性，将渐近维度与Ponomarev的Cofinal维度有关
Relating asymptotic dimension to Ponomarev's cofinal dimension via coarse proximities
论文作者
论文摘要
在本文中，我们表明，无界的适当度量空间的渐近维度在上面是由Ponomarev的拓扑空间的Cofinal尺寸的粗略类似，我们称之为粗大的辅助尺寸。我们还表明，渐近维度在下面由希格森·科罗纳（Higson Corona）的Cofinal维度界定，而Miyata，Austin和Virk的现有结果。我们通过在粗糙接近空间理论中引入几种构造来做到这一点。特别是我们引入了粗接近空间的反度。我们以一些开放的问题结尾。
In this paper we show that the asymptotic dimension of an unbounded proper metric space is bounded above by a coarse analog of Ponomarev's cofinal dimension of topological spaces, which we call the coarse cofinal dimension. We also show that asymptotic dimension is bounded below by the cofinal dimension of the Higson corona by existing results of Miyata, Austin, and Virk. We do this by introducing several constructions in the theory of coarse proximity spaces. In particular we introduce the inverse limit of coarse proximity spaces. We end with some open problems.
