建立拓扑空间的一种新方法

New Method for Building up Topological Space

拓扑学是近代数学的基础,拓扑空间的建立为近代数学的研究打下了坚实的理论基础.利用集合中满足一定条件的子集族建立拓扑空间的方法很多,文[1],[2],[3]应用开集公理建立拓扑空间,文[4]应用邻域系公理建立拓扑空间,文[5]则应用边界运算建立了拓扑空间.本文定义了不同于文[5]的边界运算,并应用这种方法建立了拓扑空间.

Topology is a important foundation of modem mathematics, the establishment of topological space stablizes theories foundation for the research of modem mathematics. There are a lot of methods using certain conditional subfamily to build up topological space, the thesis [ 1 ], [2], [3] apply open set axiom to build up topological space, the thesis [4] applies neighborhood system axiom to build up topological space, the thesis [5] applies the bound operation to build up topological space. Defines the bound operation differ from the thesis [5] and applies the method to build up the topological space.