粗维数和单位分解
Coarse dimensions and partitions of unity
摘要：
Gromov \cite{Gr$_1$}和Dranishnikov \cite{Dr$_1$}通过完全不同的方法引入了真度量空间的渐近维数和粗维数。本文统一定义了度量空间的粗维数和渐近维数，并研究了它们之间的关系，推广了Dranishnikov \cite{Dr$_1$}和Dranishnikov-Keesling-Uspienskij \cite{DKU}的结果.
英文摘要：
Gromov \cite{Gr$_1$} and Dranishnikov \cite{Dr$_1$} introduced asymptotic and coarse dimensions of proper metric spaces via quite different ways. We define coarse and asymptotic dimension of all metric spaces in a unified manner and we investigate relationships between them generalizing results of Dranishnikov \cite{Dr$_1$} and Dranishnikov-Keesling-Uspienskij \cite{DKU}.
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。
