关于非循环空间的细覆盖的神经
On nerves of fine coverings of acyclic spaces
摘要：
本文的主要结果是：（1）若空间$X$可嵌入为$\mathbb{R}^n$的胞腔子空间，则$X$允许神经同胚于$n$维立方体$\mathbb{D}^n$的任意细开覆盖;（2）每个$n$维类胞腔紧可作为胞腔子集嵌入$(2n+1)$维欧几里得空间;（3）存在一个局部紧平面集，它关于Čech同调是非循环的，并且它的细覆盖都是非循环的.
英文摘要：
The main results of this paper are: (1) If a space $X$ can be embedded as a cellular subspace of $\mathbb{R}^n$ then $X$ admits arbitrary fine open coverings whose nerves are homeomorphic to the $n$-dimensional cube $\mathbb{D}^n$; (2) Every $n$-dimensional cell-like compactum can be embedded into $(2n+1)$-dimensional Euclidean space as a cellular subset; and (3) There exists a locally compact planar set which is acyclic with respect to Čech homology and whose fine coverings are all nonacyclic.
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。
