一类新型半拓扑空间及其分离性质

A New Semi-Topological Space and Its 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。

Abstract: 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.