饱和集拓扑空间的一些性质

Some Properties of Saturated Sets Topologies

利用拓扑学的研究方法,首先给出了饱和集的交、并以及拓扑等概念。在此基础上,得到一些饱和集的拓扑性质。具体包括:饱和集拓扑空间(Xf,τ)的紧子空间在交、并运算下保持不变;利用闭映射的性质证明了若(Xf,τ)满足T2,正则以及第二可数性公理,则其在完备映射下的像也保持这种性质。

This paper discusses the important concepts of saturated sets in general topology.Using the method of topology,the concepts of intersection,union and topology of saturated sets are given.On this basis,some topological properties of saturated sets are obtained.These include:the compact subspaces of saturated sets topologies(Xf,τ)with the intersection and union operations are also a compact subspaces;if(Xf,τ)satisfy with the T2,regular and the second axiom of countability respectively,the images of per-fect map of them continue to keep the three characterizations by using the closed mapping property.