论文标题
粗糙不变$σ$的另一个视图
Another view of the coarse invariant $σ$
论文作者
论文摘要
Miller，Stibich和Moore（2010）开发了一个指标度量空间的设定值的粗糙不变$σ\ left（x，ξ\右）$。 Delyser，Labuz和Tobash（2013）提供了另一种构造$σ\ left（x，ξ\右）$的方式（作为所有顺序端的集合）。本文提供了$σ\ left（x，ξ\右）$的另一个定义。为此，我们在集合$ s \ left（x，ξ\右）的集合中介绍了一个度量标准$，$ \ left（\ mathbb {n}，0 \ right）\ to \ left（x，ξ\ right）$ $ s \ left（x，ξ\ right）$。作为一种副产品，我们的重新印度在$σ\ left（x，ξ\右）$上的一些已知定理，包括功能性和粗不平衡。
Miller, Stibich and Moore (2010) developed a set-valued coarse invariant $σ\left(X,ξ\right)$ of pointed metric spaces. DeLyser, LaBuz and Tobash (2013) provided a different way to construct $σ\left(X,ξ\right)$ (as the set of all sequential ends). This paper provides yet another definition of $σ\left(X,ξ\right)$. To do this, we introduce a metric on the set $S\left(X,ξ\right)$ of coarse maps $\left(\mathbb{N},0\right)\to\left(X,ξ\right)$, and prove that $σ\left(X,ξ\right)$ is equal to the set of coarsely connected components of $S\left(X,ξ\right)$. As a by-product, our reformulation trivialises some known theorems on $σ\left(X,ξ\right)$, including the functoriality and the coarse invariance.
