论文标题
前均匀空间的某些特性
Some properties of Pre-uniform spaces
论文作者
论文摘要
在本文中，我们介绍了前均匀空间和前毒性的概念，并研究了有关它们的一些基本属性，在此，此处的前均匀性的定义与\ cite {br2016}，\ cite {gm2007}和\ cite and \ cite and \ cite at \ cite at \ cite {k2016}的前均匀性不同。首先，我们证明每个前均匀的前血态都是规律的，并举例说明在有限的集合上存在一个前均匀的结构，因此前均匀的前血态不是离散的。此外，我们提供了三种产生（强）前均匀性的方法，即基础前的定义，一个强烈均匀均匀覆盖的家族，或一个固定前均匀的伪统计的家族。作为应用程序，我们表明每个强烈的前题学组都是完全规律的。最后，我们在集合上提出了前敏度的概念，并讨论了前敏度的某些特性。
In this paper, we introduce the notions of pre-uniform spaces and pre-proximities and investigate some basic properties about them, where the definition of pre-uniformity here is different with the pre-uniformities which are studied in \cite{BR2016}, \cite{GM2007} and \cite{K2016} respectively. First, we prove that each pre-uniform pre-topology is regular, and give an example to show that there exists a pre-uniform structure on a finite set such that the pre-uniform pre-topology is not discrete. Moreover, we give three methods of generating (strongly) pre-uniformities, that is, the definition of a pre-base, a family of strongly pre-uniform covers, or a family of strongly pre-uniform pseudometrics. As an application, we show that each strongly pre-topological group is completely regular. Finally, we pose the concept of the pre-proximity on a set and discuss some properties of the pre-proximity.
