一类新型半拓扑空间及其分离性质  

A New Semi-Topological Space and Its Separation Property

作　　者：胡西超 朱培勇[1] Xichao Hu;Peiyong Zhu(School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu Sichuan)

机构地区：[1]电子科技大学数学科学学院,四川成都

出　　处：《理论数学》2015年第4期129-135,共7页Pure Mathematics

基　　金：电子科技大学科研实训创新项目基金的经费资助。

摘　　要：2002年,A. Csaszar引入的广义拓扑空间定义仅包含拓扑空间定义条件的一半。因此,广义拓扑实际上是一类半拓扑。如果把广义拓扑相对于拓扑的另一半条件作为另一类半拓扑,那么这类半拓扑能否像广义拓扑那样具有一些良好的特征性质?本文就此问题进行研究,在这类半拓扑的点集理论和分离性质获得了一系列结果。In 2002, the concept of a generalized topological space was introduced by A. Csaszar. But it contains only half of the conditions in the definition of a topological space. Therefore, a generalized topology is a kind of semi-topologies actually. If we use the other condition of a topology which is contrary to the generalized topology as another semi-topology, can this new semi-topology be of some good properties, just like a generalized topology? This thesis is about this problem, and several results are obtained for the theories of point set and separation properties of this semi-topological space.

关 键 词：广义拓扑(上半拓扑) 下半拓扑 分离性 

分 类 号：O1[理学—数学]