粗糙空间通过映射到单纯复形的渐近维数
Asymptotic dimension of coarse spaces via maps to simplicial complexes
摘要：
众所周知，仿紧空间$X$的复盖覆盖维数至多为$n$当且仅当从$X$到单纯复形$K$的任何映射$f\colon X\to K$都能被推入其$n$骨架$K^{(n)}$中.我们用同样的思想刻画了任意粗空间的粗范畴中的渐近维数。映射$f$的连续性被替换为$f$在一致有界覆盖的元素上的变化。同样，我们可以将G.Yu的性质A推广到任意粗糙空间。
英文摘要：
It is well-known that a paracompact space $X$ is of covering dimension at most $n$ if and only if any map $f\colon X\to K$ from $X$ to a simplicial complex $K$ can be pushed into its $n$-skeleton $K^{(n)}$. We use the same idea to characterize asymptotic dimension in the coarse category of arbitrary coarse spaces. Continuity of the map $f$ is replaced by variation of $f$ on elements of a uniformly bounded cover. The same way one can generalize Property A of G.Yu to arbitrary coarse spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
