论文标题
产品空间的自忽视数量
Self-closeness numbers of product spaces
论文作者
论文摘要
CW-Complex的自相关数是由最小数字$ n $定义的同型不变性，使得每本$ x $的自图在第一个$ n $同型组的$ x $组成的$ x $ a $ x $ a $ x $的同型都是同型等效性。在本文中，我们研究了有限的笛卡尔产品的自我误度数量，并证明在某些条件下（称为可降低），产品空间的自倾性数量等于因素的最大自在性数量。研究了一系列可降低性的标准，并将结果用于确定某些特殊空间的产品空间的自邻度数量，例如摩尔空间，Eilenberg-Maclane空间或原子空间。
The self-closeness number of a CW-complex is a homotopy invariant defined by the minimal number $n$ such that every self-maps of $X$ which induces automorphisms on the first $n$ homotopy groups of $X$ is a homotopy equivalence. In this article we study the self-closeness numbers of finite Cartesian products, and prove that under certain conditions (called reducibility), the self-closeness number of product spaces equals to the maximum of self-closeness numbers of the factors. A series of criteria for the reducibility are investigated, and the results are used to determine self-closeness numbers of product spaces of some special spaces, such as Moore spaces, Eilenberg-MacLane spaces or atomic spaces.
