理论数学

Vol.5 No.4 (July 2015)

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 :电子科技大学数学科学学院,四川 成都

 

关键词:

广义拓扑(上半拓扑)下半拓扑分离性Generalized Topology (Sup-Semi-Topology) Inf-Semi-Topology Separation Property

 

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.

文章引用:

胡西超 , 朱培勇 (2015) 一类新型半拓扑空间及其分离性质。 理论数学, 5, 129-135. doi: 10.12677/PM.2015.54020

 

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