拓扑空间的敏感性

Sensitivities for topological spaces

文章研究了一致空间、Hausdorff空间和度量空间上的一些敏感性质。分别用Hausdorff空间中的有限开覆盖和一致空间中的“从”介绍了n-敏感、敏感串和局部proximal串等概念,证明了这3个概念两种版本的定义在紧致的Hausdorff空间上分别是互相等价的。更进一步地,如果在一个紧致的度量空间上,那么这3个概念两种版本的定义与它们的标准定义也分别是互相等价的。

In this paper,we study the sensitive properties on uniform space,Hausdorff space and metric space,introduce the notions of n-sensitivity,sensitive tuple,and local proximal tuple in terms of finite open covers and for Hausdorff topological spaces and entourages for uniform spaces.We show that the two definitions for each notion are equivalent in compact Hausdorff spaces and further they are equivalent to their standard definitions in compact metric spaces.